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# Which of the following is equal to

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following is equal to [#permalink]

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11 Jan 2018, 00:49
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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
[Reveal] Spoiler: OA

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Which of the following is equal to [#permalink]

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11 Jan 2018, 02:18
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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)
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Re: Which of the following is equal to [#permalink]

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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
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Re: Which of the following is equal to [#permalink]

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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.

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

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