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# Which of the following is equivalent to √3+√2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Which of the following is equivalent to √3+√2?  [#permalink]

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30 Mar 2017, 01:23
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25% (medium)

Question Stats:

68% (01:17) correct 32% (01:28) wrong based on 192 sessions

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Which of the following is equivalent to √3+√2?

A. $$√5$$
B. $$\sqrt{5+2√6}$$
C. $$\sqrt{6+2√5}$$
D. $$\sqrt{5-2√6}$$
E. $$\sqrt{5+4√6}$$

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"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" ##### Most Helpful Community Reply Senior Manager Joined: 19 Apr 2016 Posts: 274 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: Which of the following is equivalent to √3+√2? [#permalink] ### Show Tags 30 Mar 2017, 01:29 11 4 MathRevolution wrote: Which of the following is equivalent to √3+√2? A. $$√5$$ B. $$\sqrt{5+2√6}$$ C. $$\sqrt{6+2√5}$$ D. $$\sqrt{5-2√6}$$ E. $$\sqrt{5+4√6}$$ let x = √3+√2 ------------------I on squaring both sides, $$x^2 = (√3+√2)^2$$ $$x^2 = (√3)^2 + (√2)^2 + 2*(√3√2)$$ $$x^2 = 3 + 2 + 2√6$$ $$x^2 = 5 + 2√6$$ taking square root on both sides x = $$\sqrt{5+2√6}$$ √3+√2 = $$\sqrt{5+2√6}$$ (from I) Hence option B is correct Hit Kudos if you liked it ##### General Discussion Manager Status: GMAT...one last time for good!! Joined: 10 Jul 2012 Posts: 59 Location: India Concentration: General Management GMAT 1: 660 Q47 V34 GPA: 3.5 Re: Which of the following is equivalent to √3+√2? [#permalink] ### Show Tags 30 Mar 2017, 10:58 MathRevolution wrote: Which of the following is equivalent to √3+√2? A. $$√5$$ B. $$\sqrt{5+2√6}$$ C. $$\sqrt{6+2√5}$$ D. $$\sqrt{5-2√6}$$ E. $$\sqrt{5+4√6}$$ √3+√2=1.73+1.41=3.14 A quick look tells us that only B and C are close. 25^2=625. so sqrt(6) is approx 2.4; hence B=5+4.8=9.8 C=6+2*2.2>10.4 B is closer to our 3.14^2 _________________ Kudos for a correct solution Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is equivalent to √3+√2? [#permalink] ### Show Tags 02 Apr 2017, 17:22 ==> You get $$√a+√b=\sqrt{a+b+2√ab}$$ because if you square both sides, you get $$a+b+2\sqrt{ab}$$ on both sides. Thus, you get $$√3+√2=\sqrt{5+2√6}$$. The answer is B. Answer: B _________________ 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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Re: Which of the following is equivalent to √3+√2?  [#permalink]

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01 Mar 2018, 09:54
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Top Contributor
MathRevolution wrote:
Which of the following is equivalent to √3+√2?

A. $$√5$$
B. $$\sqrt{5+2√6}$$
C. $$\sqrt{6+2√5}$$
D. $$\sqrt{5-2√6}$$
E. $$\sqrt{5+4√6}$$

KEY CONCEPT: If we take a positive number, square it and then take the square root of the result, we'll get back to the same number we started with.
For example...
Take: 5
Square it to get: 25
Take the square root: √25
Evaluate: 5

Now let's answer the question:
Take: √3+√2
Square it to get: (√3+√2)(√3+√2)
Use FOIL to expand : 3 + √6 + √6 + 2
Simplify: 5 + 2√6
Take the square root: √(5 + 2√6)

Answer: B

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Re: Which of the following is equivalent to √3+√2? &nbs [#permalink] 01 Mar 2018, 09:54
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# Which of the following is equivalent to √3+√2?

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