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Which of the following is equal to 1/(√3−√2)^2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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03 Jan 2017, 18:32
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74% (00:59) correct 26% (00:47) wrong based on 99 sessions

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Which of the following is equal to $$1/(√3−√2)^2$$?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 11 Nov 2015 Posts: 20 Re: Which of the following is equal to 1/(√3−√2)^2? [#permalink] Show Tags 03 Jan 2017, 19:52 $$\frac{1}{(√3−√2)^2}$$=$$\frac{1*(√3+√2)^2}{(√3−√2)^2*(√3+√2)^2}$$ ......multiply denominator and numerator by $$(√3+√2)^2$$ =$$\frac{(√3)^2−2(√2)(√3)+(√2)^2}{(√3^2−√2^2)^2}$$ =$$3-2√6+2$$ =$$5+2√6$$ E Manager Status: Preparing for GMAT!! Joined: 11 Oct 2015 Posts: 137 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 660 Q47 V34 GMAT 2: 700 Q48 V38 GPA: 3.1 WE: General Management (Entertainment and Sports) Re: Which of the following is equal to 1/(√3−√2)^2? [#permalink] Show Tags 04 Jan 2017, 12:57 By Simplifying=> 1/(5-2sqrt6) By rationalising=>(5+2sqrt6)/(25-24) =>5+2sqrt6 E. Sent from my SM-G935F using GMAT Club Forum mobile app _________________ Yours, Siva Rama Krishna Meka Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6040 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is equal to 1/(√3−√2)^2? [#permalink] Show Tags 04 Jan 2017, 18:56 $$1/((√3−√2)^2)=1/(3+2−2√3 √2)=1/(5−2√6)*((5+2√6))/((5−2√6)(5+2√6))=((5+2√6))/(5^2−〖(2√(6))〗^2 )=((5+2√6))/(25−24)=5+√6$$ The answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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05 Aug 2018, 19:03
1
MathRevolution wrote:
Which of the following is equal to $$1/(√3−√2)^2$$?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

I. Simplify and rationalize
Simplify:
$$\frac{1}{(√3−√2)^2}$$
$$\frac{1}{(√3−√2)(√3−√2)}$$
$$\frac{1}{3-2√6+2}=\frac{1}{5-2√6}$$

Rationalize with conjugate: $$5+2√6$$
$$(\frac{1}{5-2√6}*\frac{5+2√6}{5+2√6})=\frac{5+2√6}{25-(4*6)}$$

$$\frac{5+2√6}{25-24}=\frac{5+2√6}{1}=5+2√6$$

Rationalize all at once
The denominator has two "copies" of $$(a-b)$$, one of the factored terms of a difference of perfect square $$(a+b)(a-b)=a^2-b^2$$.

If we multiply by two copies of $$(a+b)$$ -- the conjugate of the denominator, squared -- we will create two differences of perfect squares that in this instance are integers.

$$\frac{1}{(√3−√2)^2}=\frac{1}{(√3−√2)(√3−√2)}$$

$$\frac{1}{(√3−√2)(√3−√2)}*\frac{(√3+√2)^2}{(√3+√2)^2}$$

$$\frac{1}{(√3−√2)(√3−√2)}*\frac{(√3+√2)(√3+√2)}{(√3+√2)(√3+√2)}$$

$$\frac{(√3+√2)(√3+√2)}{(√3−√2)(√3+√2)(√3−√2)(√3+√2)}$$

$$\frac{3+2√6+2}{(3-2)(3-2)}=\frac{5+2√6}{(1*1)}=5+2√6$$

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Which of the following is equal to 1/(√3−√2)^2? &nbs [#permalink] 05 Aug 2018, 19:03
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