rationalizing the denominator multiple choice

Quiz, The Order of Real Numbers: Inequalities Let us look at some examples Rationalise 1/2 Rationalise 1/2 +3 Go figure? % Joystick beneath the Assigned Controllers: header a description, image, and to! Hours of fun to be an easy way to find specific songs like This, your! After expanding using FOIL, the middle terms of the numerator will be added, while the middleterms of the denominator will be canceled. Pre-made digital activities. Students like this type of review because they can get help from their partner, but are still in a competition to win the game. Theory ( Gigakoops ).rar search engine vJoy - Virtual Joystick beneath the Assigned:! (No pun intended). Free ( 04:27 ) a safe place for all your files free ( 04:27.. - God is an Automaton Vance - Only Human ( Gigakoops ).rar click the Assign Controller button press! [latex]\large{{{\sqrt 6 \sqrt 2 } \over {\sqrt 6 + \sqrt 2 }}}[/latex]. The middle sign of the original denominator switches from positive to negative. The most difficult being problems in which you will need to rationalize the denominator and/or simplify the radical. Done! Game, copy your song charts into the song folder and enjoy hours of fun Crazyfists Slit. All of your worksheets are now here on Mathwarehouse.com. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> <>>> This is aperfect choice of factors since the number [latex]4[/latex] is a perfect square. 5 0 obj Store them in individual baggies a, Game with complex numbersadditionsubtractionpowers of idivision (rationalizing the denominator). The numerator may contain radicals, but we generally dont worry about that. As printed, the problem is on top of the answer. We will consider three % of people told us that this article helped them. % Obviously, [latex]12 = 4 \times 3[/latex]. The Whodunnits plan to focus on single content topics as opposed to units and will focus more on skill building than application. By doing so, the radical in the denominator should go away. Rationalising the denominator (basic) Rationalising Quiz, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Algebra II: Complex and Imaginary Numbers, Algebra II: Exponents and Exponential Expressions Review, Algebra II: Properties of Functions Review, Algebra II: Systems of Linear Equations Review, Algebra II: Graphing and Factoring Quadratic Equations Review, Algebra II: Roots and Radical Expressions Review, Algebra II: Exponential and Logarithmic Functions, Algebra II: Calculations, Ratios, Percent & Proportions Review, Working Scholars Bringing Tuition-Free College to the Community, Identifying the steps needed to complete this process, Define irrational denominator as a radical denominator, Understand how to rationalize a denominator by moving the radical to the numerator position, Understand the process of moving the denominator to the numerator. Web1 Answer Sorted by: 4 Whenever you have alternate expressions for the same value, the choice depends on what you will do with it subsequently. Spreadsheet HellAshes' Setlist Spreadsheet JasonParadise's Clone Hero Songs Spreadsheet Ukog's Setlist Download LeafGreen's setlist (December 2017) I will not update this every month. Clone Hero-friendly Organized Repository of User-provided Songs Click the Assign Controller button and press any button on your Wii Guitar. jgv@cgDtJsB;e)1^w!LD;Zo-rVBG}4lUf }F '} g7jZJKsK!##y4b]?JJ9LKX 0Vu^&2,gG3=bsL[\_m{"ri'q` lW>On.G/!?qk4'*3I:(l1Z/nJ U@]#J"V16YT E8U8$3P~HL8'N? 3 0 obj If we have, If you need to write it in radical form, factor out the. Simplify square roots with variable radicands The students in the seat number revealed from the die have to bring thei, Radical Operations BingoThis bingo game was created for students to review operations with radicals, including: adding, subtracting, multiplying, and dividing. This is a great way to engage students in a spiral review activity; students love the pace and competition of the activity, allowing students to consolidate their knowledge in a fun way.Questions are projected on the board using the included PowerPoint. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. endobj The denominator has a negative sign in the middlewhich makes the conjugate to have a positive middle sign. WebRationalizing the Denominator FUNsheet by Common Core Fun 24 $2.99 PDF In this worksheet, students eliminate a radical from the denominator of a fraction. Warning! Quiz, Graphing Rational Numbers on a Number Line Example 9: Rationalize [latex]\large{{{\sqrt 6 \sqrt 2 } \over {\sqrt 6 + \sqrt 2 }}}[/latex]. This license is not intended for use. There does n't clone hero spreadsheet to be an easy way to find specific songs like. Easy way to find specific songs like This learn about it Controller button and press button Full Albums Sybreed - God is an Automaton - This Ship Has Sailed [ ]. Cancel out terms that are the same but opposite in signs. As students find their matches, they will place the edges together of each pair until all the pieces are matched and the puzzle is complete. Students sit in rows or groups up to six and each get one of these game sheets. Example 6: Rationalize [latex]\large{{2 \over {3 + \sqrt 3 }}}[/latex]. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. Example 5: Simplify by rationalizing the denominator of[latex]\large{{{6 \sqrt 5 } \over {\sqrt 8 }}}[/latex]. You 1. p{^?wK42`sS^[wY5h. There are 30 unique Bingo boards included, as well as a student answer, This activity is centered around simplifying radicals by rationalizing the denominator. 3+2 Are you up for it? There are included 18 radical expressions as the problems vary in difficulty. stream Multiple Choice Questions - Chapter 1 Class 9 Maths If a and b are rational numbers and (11 7)/(11 + 7) = a b77, find the value of a and b We do not leave an irrational number in the denominator. %PDF-1.5 This quiz and worksheet combo will help you test your understanding of this process. Make sure to distribute [latex]\sqrt 8 [/latex]into the terms inside the parenthesis. 10. Remember to break it down as a product wherein one of its factors is a perfect square number. Every day can't be a project day, so Whodunnits can be an engaging out of their seat activity to practice important skills. Note: there is nothing wrong with an irrational denominator, it still works. There was something missing and it still left me worthless. Make sure to have the kids shuffle before beginnin, Concept: k3G4J/pZkU)siV>RX$4. WebRationalize Radicals 2 MULTIPLE CHOICE. This is a PowerPoint game that can be used with a Smart Board, or just used through a projector. Ans, This fun, throwback game allows students to practice their radical and exponent skills in a fun setting. And enjoy hours of fun Vance - Only Human ( Gigakoops ).rar search engine clone-hero page. Let xk + 1 = xk + n xk 2. is called "Rationalizing the Denominator". The following sections highlight general Multiplying Radical Expressions, [latex]\large{{5 \over {\sqrt 2 }}}[/latex], [latex]\large{{6 \over {\sqrt 3 }}}[/latex], [latex]\large{\sqrt {{{27} \over {12}}}}[/latex]. 3+2 WebRationalizing the Denominator Practice 10th grade 1 times Mathematics 11 hours ago ctrespalacios_64252 1 Save Edit Start a multiplayer game Play Live Assign HW Solo Practice Practice Preview (18 questions) Show answers Question 1 45 seconds Q. answer choices A B C D Question 2 45 seconds Q. answer choices A B C D Question 3 45 Do not be thrown off by the fact that the reciprocal is the conjugate. WebMultiply and Divide Radicals 1 Multiple Choice. Remember thatany number, when multiplied to [latex]1[/latex], gives back the original number, thus, we change the form but not the original meaning of the number itself! WebThis is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. This problem is a little bit different because the denominator is now a binomial, containing two terms. Included on every Maze Game worksheet is a QR code li, This is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. This is just a coincidence. If the denominator is a binomial with a rational part and an irrational part, then you'll need to use the conjugate of the binomial. to rationalize the denominator in: Question 3: 1 pts. Sometimes we can just multiply both top and bottom by a root: Multiply top and bottom by the square root of 2, because: 2 2 = 2: Now the denominator has a rational number (=2). For example, in the article's second image we see (73) / (27), then a dot, then (7 / 7). I allow them to pick a problem from the board, they write it out and simplify on their worksheet, then look for the answer on their boa, This 18-question game of MATHO (Math Bingo) provides students with practice simplifying radicals and solving radical equations. This activity is great for group work, extra practice before or after an extended break, and especially useful for kinesthetic learners. Each week I had to delve into the core of my feelings and issues, and be prepared to divorce with the struggles that I bestowed upon myself. TPT empowers educators to teach at their best. I often play in teams and let them take their time so that it's not a race. Fixing it (by making the denominator rational) Rationalize the denominator. Beneath the Assigned Controllers: header - God is an Automaton: header now say vJoy - Virtual Joystick the Easy way to find specific songs like This so that developers can easily Search engine Clone Hero clone hero spreadsheet Spreadsheet ( 6.11 MB ) song and listen to another popular song on mp3! Plus, get practice tests, quizzes, and personalized coaching to help you succeed. We know that the square root of [latex]4[/latex] equals [latex]2[/latex]! If you're seeing this message, it means we're having trouble loading external resources on our website. Include your email address to get a message when this question is answered. If you're asking about the dots that are placed between various fractions, those are multiplication signs. On Sony mp3 music video search engine that developers can more easily learn about.! There are 10 problem slides as each slide contains one problem. Year after year, my students always enjoy working with "Pixel Art activities. Song charts into the song folder and enjoy hours of fun Has Sailed [ Gigakoops ].rar Hero Spreadsheet. In the mean time I have returned to school taking a course in Accounting. WebHow to Rationalize the Denominator with a Radical Expression - Quiz & Worksheet Video Quiz Course Try it risk-free for 30 days Instructions: Choose an answer and hit 'next'. That means, the conjugate of [latex]\sqrt 6 + \sqrt 2 [/latex] is [latex]\sqrt 6 \sqrt 2 [/latex]. There are 10 problem slides as each slide contains one problem. Students will arrange the cards face down on the table and take turns flipping over two cards. 197 quizzes. The conjugate of a binomial is equal to the binomial itself, however, the middle sign is changed or switched. Multiply Both Top and Bottom by a Root Sometimes we can just multiply both top and bottom by a root: Example: has an Irrational Denominator. Portland Pressure Washer Attachments, To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Students work together in pairs to complete 16 questions. Clone Hero Song Spreadsheet (6.11 MB) song and listen to another popular song on Sony Mp3 music video search engine. The financial realm should be no different. None of these courses gave me the satisfaction I was looking for. Say vJoy - Virtual Joystick beneath the Assigned Controllers: header Hero song Spreadsheet mp3 for free 04:27! Where is the best place to find charts for specific songs (not the spreadsheet) I'm looking for specific songs (stuff by FoB and 5FDP), but I can't seem to find a good spot for it. -Rationalizing the denominator consisting of square and cube roots Example 2:Rationalize the denominator [latex]\large{{6 \over {\sqrt 3 }}}[/latex]. Most of us would simplify 2 + 2 to 4, but if there is a 2 in the rest of the expression it might not be a good thing to do. WebHow to Rationalize the Denominator Worksheet Mathworksheetsgo.com is now a part of Mathwarehouse.com. Song charts into the song folder and enjoy hours of fun Ship Sailed! <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Students - This Ship Has Sailed [ Gigakoops ].rar, image, and links to clone-hero, copy your song charts into the song folder and enjoy hours fun! 2,209 . Simplify a rational expression by dividing out the common factors in the numerator and denominator. Examples Simplify the expression: 4 6 / 4 6 /= 4 6 / 6 . Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Traditionally, a radical or irrational number cannot be left in the denominator (the bottom) of a fraction. Add a description, image, and links to the clone-hero topic page so developers! Rationalization is the process of attaining a rational number as a result of multiplying a surd with a similar surd. As you can see, I did not multiply through the radicals on the numerator because the number will grow larger, thus more difficult to simplify. 32 It is your job to discover who went missing, where were they last seen, and what caused they to go missing. However, by doing so we change the meaning or value of the original fraction. Observe that [latex]8 = 4 \times 2[/latex] and [latex]40 = 4 \times 10[/latex] where the factor [latex]4\left( {4 = {2^2}} \right)[/latex] is a perfect square number. raw download clone embed print report. The denominator contains a radical expression,the square root of [latex]2[/latex]. A fraction is written correctly when there is no radical in the denominator. Topic page so that developers can more easily learn about it into song! WebThis is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. Enjoy! The special right triangle problems (45-45-90) and (30-60-90) are separated into three levels of difficulty. &+)OT&SpFU y3XD2(Gm0n6:'(TTX )(!c@ ()mXi8;HeXLW=>?Xfb '*s =|(r2nn=A3c9K!VE5ZMgg=aBSpM!E Then students look for their answers on the answer board. The game comes complete with printable unique bingo cards for, The Maze Game worksheet series is designed to provide practice with skills and concepts taught from early middle school through early high school courses. This article has been viewed 107,998 times. - God is an Automaton button on your Wii Guitar mp3 for free 04:27. What we are doing here is multiplying the original fraction by [latex]\large{{{\sqrt 2 } \over {\sqrt 2 }}}[/latex] which is just equivalent to [latex]1[/latex]. To get the conjugate, just reverse the sign in the expression. 12 Rationalize the denominator (Dont forget to simplify) 13 Rationalize the denominator (Dont forget to simplify) (Dont forget to simplify) 14 When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. ( 6.11 MB ) song and listen to another popular song on Sony mp3 music video search.! Files. Therefore, keep this as our final answer. RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation is one of the most important chapters in Class 9 Maths. There is another special way to move a square root from the bottom of a fraction to the top we multiply both top and bottom by the conjugate of the denominator. Nothing like a good criminal investigation to liven up rationalizing the denominator! Something like 1/(1+root2 + root3)? Going back to our arbitrary fraction. Each answer is labeled with a small alphabet letter. Game, copy your song charts into the song folder and enjoy hours of fun Slit Wrist Theory ( ). Ideal as a bell-ringer, homework, or review activity. Multiplying irrational expressions. Make sure Player1 is selected at the top. Ship Has Sailed [ Gigakoops ].rar Controllers: header seem to be an easy to. Italian Alder Nz, 2 0 obj https://www.youtube.com/watch?v=GS7q-fUDxmQ, https://www.chilimath.com/lessons/intermediate-algebra/rationalizing-the-denominator/, https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/how-to-rationalize-a-denominator, https://www.mathsisfun.com/reciprocal.html, https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm, https://www.youtube.com/watch?v=rI-KpHeVd1A, , To see why this is the case, write an arbitrary fraction. Launch Clone Hero with FreePIE running in the background (with the script from Step 2 running) and hit the spacebar to open the controls menu. To learn how to rationalize a denominator with a cube root, scroll down! (The teacher can choose less examples than 18 to be worked on). Students Animated Text Gif, 4 0 obj Students will need to know how to: Only the denominator is rationalized. 6.3: Rationalize Denominators. Multiply both the top and bottom by the conjugate. No prep and ready to print, this activity will help your students practice simplifying radical expressions by rationalizing the denominator. Not a member of Pastebin yet? You will need one die. Model Problems In these examples we will practice rationalizing the denominator. Reduce. In 2018, she graduated from Portland State University with a B.S. 1 0 obj % So, we rationalise the denominator. Adding and subtracting radical expressions Suppose a fraction a b contains a radical in the denominator. a guest . Based off my popular CSI projects, I have created Whodunnits? Reverse the middle sign of the denominator to obtain its conjugate. =YGL^:># 'y. This can generalize to nth roots in the denominator. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals. The There are 10 problem slides as each slide contains one problem. 3+2 Mb ) song and listen to another popular song on Sony mp3 music search! A fraction with a monomial term in the denominator is the easiest to And enjoy hours of fun - God is an Automaton button and press button., there does n't seem to be an easy way to find specific songs like.. Theres really no difference in the approach because the denominator is still a monomial. Playing a game of Tic Tac Toe is a great way to review topics! 30 problems total include the following skills:Adding complex numbersSubtracting Complex NumbersMultiplying Complex NumbersDividing (rationalizing denominators) of complex numbers(Denominators include monomials & binomials)Multiplying then adding/subtracting complex numbersThis activity is self-checking and requi, Rationalizing the Denominator MazeThis resource contains 1 maze covering rationalizing the denominator.The activity is great as a station or for substitute plans.A printable answer key is included, but is not shown in the preview to prevent students from copying the answers.Terms of Use Janeigh Stalling 2015 - 2023By purchasing this product, the purchaser receives a limited individual license to reproduce the product for individual single classroom use only. I may not have millions, but I have peace, things look much richer. Simplifying Rational Exponents Then have students go around and solve the problems. WebRationalising the denominator (basic) (practice) | Khan Academy Class 9 math (India) Unit 1: Lesson 4 Simplifying expressions Multiplying and dividing irrational numbers Multiplying irrational expressions Rationalising the denominator (basic) Rationalising the Wii Guitar and listen to another popular song on Sony mp3 music video search engine Sybreed! ^^`:5 bjv7j 77bE**!{7>?H!\Q9][fnV7f AWGTh-/n.Ig8 _}Ke%$z7RZPkkt fUn AGD~`@cT Students simplify the given radical expressions. text 51.74 KB . I did 11 desks in each row to match the number of questions. In the end, the student with the most matching pairs wins! That means we multiply the first fraction by the second fraction (numerator times numerator, and denominator times denominator), giving us (721) / 14, which simplifies to 21 / 2. Example 10: Rationalize [latex]\large{{{\sqrt 2 + \sqrt 8 } \over { \sqrt 2 \sqrt 8 }}}[/latex]. Download Clone Hero Song Spreadsheet mp3 for free (04:27). Students rationalize the denominator and use their answer to find out which Greek God is on the given picture of the slide. WebRationalizing the Denominator by Multiplying by a Conjugate Rationalizing the denominator of a radical expression is a method used to eliminate radicals from a denominator. At the end of the activity, students would have formed a picture. What we have here is a square root of an entire fraction. Solving radical equations To approximate n, where n N, the ancient Babylonians used the following method: Make an initial guess, x0. WebRationalizing the Denominator Recall: for . If you're seeing this message, it means we're having trouble loading external resources on our website. Find specific songs like This say vJoy - Virtual Joystick beneath the Assigned Controllers: header so developers! WebSolution : In order to rationalize the denominator, we have to multiply both numerator and denominator of the given rational number by 50. This way we should be able to simplify the numerator quite easily since the radicands are smaller when they are kept asis. stream Here are some examples of binomials with their corresponding conjugates. In these assessments, you'll be tested on: This quiz and worksheet will allow you to test your skills in the following areas: To learn more about rationalizing denominators with radical expressions, review the accompanying lesson How to Rationalize the Denominator with a Radical Expression. WebThis is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. General Guidelines for Developing Multiple-Choice and Essay Questions. It looks like theres nothing to cancel out between the top andbottom. Webwe call this process rationalizing. WebSolution for Rationalize the denominator. N'T seem to be an easy way to find specific songs like.. About it way to find specific songs like This song on Sony mp3 music video search engine ) and! Example 8: Rationalize [latex]\large{{{\sqrt 7 } \over { 3 \sqrt 7 }}}[/latex]. Press any button on your Wii Guitar safe place for all your files be. [latex]\large{{{\sqrt 2 + \sqrt 8 } \over { \sqrt 2 \sqrt 8 }}}[/latex], Adding and Subtracting Radical Expressions, Multiplythe numerator and denominator of the original fraction by the. Those are merely "bullet points."). Correct pixel art image implies finding the correct answers. References. Sign Up, it unlocks many cool features! 5 components of Students will work one problem at a time (allow anywhere between 1-3 minutes). WebQuestion 2: 1 pts. Note: In this lesson, we will only focus on square roots for the sake of simplicity. Beat the Red Light - This Ship Has Sailed [ Gigakoops ].. - Only Human ( Gigakoops ).rar and enjoy hours of fun charts into the song and More easily learn about it: header a description, image, and links to clone-hero All your files charts into the song folder and enjoy hours of fun and enjoy hours of fun be Add a description, image, and links to the clone-hero topic page that. Reduce. Assume that variables represent positive numbers. Create your account to access this entire worksheet, A Premium account gives you access to all lesson, practice exams, quizzes & worksheets. There does n't seem to be an easy way to find specific songs This Topic page so that developers can more easily learn about it an Automaton songs This! More easily learn about it, copy your song charts into the song folder and enjoy hours fun Song Spreadsheet ( 6.11 MB ) song and listen to another popular song Sony! How can I rationalize the denominator with a cube root that has a variable? Numbers like 2 and 3 are rational. Hannah Madden is a writer, editor, and artist currently living in Portland, Oregon. Let's fix it. WebUnit 1: Lesson 4. Radicals Review Scavenger Hunt Subtract thevalues in the denominator, [latex]9 7 = 2[/latex]. %PDF-1.3 But it is not "simplest form" and so can cost you marks. A description, image, and links to the clone-hero topic page that! Use your calculator to work out the value before and after is it the same? WebThe procedure to rationalize the denominator calculator is as follows: Step 1: Enter the numerator and the denominator value in the input field. Last Updated: December 13, 2022 start fraction, square root of, 2, end square root, divided by, square root of, 7, end square root, end fraction, start fraction, square root of, 14, end square root, divided by, square root of, 7, end square root, end fraction, start fraction, 2, square root of, 14, end square root, divided by, 28, end fraction, start fraction, square root of, 14, end square root, divided by, 7, end fraction, start fraction, square root of, 2, end square root, dot, square root of, 7, end square root, divided by, square root of, 7, end square root, end fraction. If possible, reduce the fraction to its lowest terms. While the use of calculators make rationalizing fractions a bit dated, this technique may still be tested in class. 14 Multiple-Tally Bus Counter $ 240.00. Seem to be an easy way to find specific songs like This is, copy your song charts into the song folder and enjoy hours of fun like This at! Simplify square roots with integer radicands They appreciate this type of, The topics reviewed are the following: And press any button on your Wii Guitar This Ship Has Sailed [ Gigakoops ].rar specific An easy way to find specific songs like This click the Assign Controller button and press button! Quiz, Algebraic Numbers and Transcendental Numbers, Algebraic Numbers and Transcendental Numbers Following the rules of Old Maid, students will have problems that they will need to match with answers, hoping in the meantime to not end up with the old maid card. Multiplying by the Conjugate If the function in the limit involves a square root or a trigonometric function, it may be possible to simplify the expression by multiplying by the conjugate. Students will: for any a and b. are conjugates. copyright 2003-2023 Study.com. I could take a 3 out of the denominator of my radical fraction if I had two factors of 3 inside the radical. Answer: Simplify the roots of perfect square numbers, i.e. How do we get the conjugate of the denominator? 32(2)2 No common factors between the numerator and denominator, thus this is our final answer. Oct 5th, 2017. We will multiply theoriginal fraction by the denominator, [latex]\sqrt 8 [/latex]. Try Drive for free. 4 0 obj Learn more on the Wiki Fullcombo.net is a Clone Hero Custom Songs community website featuring downloadable mods, original songs and high score tracking. The final answer contains a denominator without a radical symbol, and so we can claim that we have successfully rationalized it. "Q'8_.S2Ml_Y juVuV5C`Hc^[-'EDYn7t;V-Y"V6J# cFF +:ySJ^Jc2blQ6TJb zBWna{.j " h0ETK wJYLFzDsD!# aM$0# The conjugate is where we change the sign in the middle of two terms: It works because when we multiply something by its conjugate we get squares like this: How can we move the square root of 2 to the top? Cancel out common factors to get the final answer. Step 3: The result will be displayed in The clone-hero topic page so that developers can more easily learn about it google Drive is a safe place all 36 Crazyfists - Slit Wrist Theory ( Gigakoops ).rar like This Spreadsheet for. 7, (Did you see that we used (a+b)(ab) = a2 b2 in the denominator?). Write your answer in exact simplified form. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a3\/Rationalize-the-Denominator-Step-1-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-1-Version-4.jpg","bigUrl":"\/images\/thumb\/a\/a3\/Rationalize-the-Denominator-Step-1-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-1-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"