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# Which of the following is equal to

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6811
GMAT 1: 760 Q51 V42
GPA: 3.82
Which of the following is equal to  [#permalink]

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11 Jan 2018, 00:49
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:09) correct 40% (02:15) wrong based on 90 sessions

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[GMAT math practice question]

Which of the following is equal to $$(\sqrt{16+4√15}+\sqrt{16-4√15})^2$$

A. 10
B. 12
C. 24
D. 36
E. 40

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3334 Location: India GPA: 3.12 Which of the following is equal to [#permalink] ### Show Tags 11 Jan 2018, 02:18 2 MathRevolution wrote: [GMAT math practice question] Which of the following is equal to $$(\sqrt{16+4√15}+\sqrt{16-4√15})^2$$ A. 10 B. 12 C. 24 D. 36 E. 40 $$(\sqrt{16+4√15}+\sqrt{16-4√15})^2$$ = $$16+4√15+16-4√15+2\sqrt{(16+4√15)(16-4√15)}$$ (because $$(a + b)^2 = a^2 + b^2 + 2*a*b$$) = 32 + 2$$\sqrt{256 - 16*15}$$ (because $$(a+b)(a-b)= a^2 - b^2$$) = $$32+8 = 40$$(Option E) _________________ You've got what it takes, but it will take everything you've got Manager Joined: 23 Feb 2017 Posts: 59 Re: Which of the following is equal to [#permalink] ### Show Tags 11 Jan 2018, 04:19 $$(a+b)^2$$ = $$a^2$$ +$$b^2$$ +2*a*b ($$\sqrt{16+4√15}$$+$$\sqrt{16−4√15}$$)^2 = 16+4√15 + 16−4√15 +2* $$\sqrt{16+4√15}$$ *$$\sqrt{16−4√15}$$ (a+b)(a-b) = $$a^2$$-$$b^2$$ =32 + 2* $$\sqrt{(16*16 - 4*4*15)}$$ =32 + 2* $$\sqrt{(16*(16 -1)5)}$$ =32+ 2*4 =40 Ans. E _________________ +1 Kudos if you find it helpful. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6811 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is equal to [#permalink] ### Show Tags 14 Jan 2018, 17:32 => $$(\sqrt{16+4√15}+\sqrt{16-4√15})^2$$ $$= (\sqrt{16+2√60}+\sqrt{16-2√60})^2$$ $$=(√10 +√6 + √10-√6))^2$$ $$=(2√10)^2$$ $$=4*10$$ $$= 40$$ Therefore, 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$149 for 3 month Online Course"
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Re: Which of the following is equal to  [#permalink]

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18 Jan 2018, 07:44
MathRevolution wrote:
[GMAT math practice question]

Which of the following is equal to $$(\sqrt{16+4√15}+\sqrt{16-4√15})^2$$

A. 10
B. 12
C. 24
D. 36
E. 40

We can use the quadratic identity of (x + y)^2 = x^2 + y^2 + 2xy, in which:

√(16 + 4√15) = x and √(16 - 4√15) = y; thus:

x^2 = 16 + 4√15

y^2 = 16 - 4√15

2xy = 2√[(16 + 4√15)(16 - 4√15)]

Notice that (16 + 4√15)(16 - 4√15) is in the form of a difference of squares, and thus:

(16 + 4√15)((16 - 4√15) = 16^2 - (4√15)^2 = 256 - 240 = 16

So 2√(16 + 4√15)((16 - 4√15) = 2√16 = 2 x 4 = 8

Thus, the final value is 16 + 4√15 + 16 - 4√15 + 8 = 40.

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Re: Which of the following is equal to &nbs [#permalink] 18 Jan 2018, 07:44
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