[GMAT math practice question]
Which of the following is equal to $$^{\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2}$$
A. 10
B. 12
C. 24
D. 36
E. 40
Which of the following is equal to
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- Max@Math Revolution
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Hi Max@Math Revolution,Which of the following is equal to $$^{\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2}$$
A. 10
B. 12
C. 24
D. 36
E. 40
Let's take a look at your question.
$$\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2$$
Evaluating the square,
$$=\left(\sqrt{16+4\sqrt{15}}\right)^2+2\left(\sqrt{16+4\sqrt{15}}\right)\left(\sqrt{16-4\sqrt{15}}\right)+\left(\sqrt{16-4\sqrt{15}}\right)^2$$ $$=16+4\sqrt{15}+2\left(\sqrt{\left(16\right)^2+\left(4\right)^2\left(15\right)}\right)+16-4\sqrt{15}$$
$$=16+2\left(\sqrt{256-\left(16\right)\left(15\right)}\right)+16$$
$$=32+2\left(\sqrt{16}\right)$$
$$=32+2\left(4\right)$$
$$=32+8=40$$
Therefore, Option E is correct.
Hope it helps.
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- Max@Math Revolution
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$$\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2$$
= $$\left(\sqrt{16+2\sqrt{60}}+\sqrt{16-2\sqrt{60}}\right)^2$$
= $$\left(\sqrt{10}+\sqrt{6}+\sqrt{10}-\sqrt{6}\right)^2$$
= $$\left(2\sqrt{10}\right)^2$$
$$=40\cdot10$$
=40
Therefore, the answer is E.
Answer: E
= $$\left(\sqrt{16+2\sqrt{60}}+\sqrt{16-2\sqrt{60}}\right)^2$$
= $$\left(\sqrt{10}+\sqrt{6}+\sqrt{10}-\sqrt{6}\right)^2$$
= $$\left(2\sqrt{10}\right)^2$$
$$=40\cdot10$$
=40
Therefore, the answer is E.
Answer: E
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We can BALLPARK.Max@Math Revolution wrote:[GMAT math practice question]
Which of the following is equal to $$^{\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2}$$
A. 10
B. 12
C. 24
D. 36
E. 40
16 + 4√15 = 16 + 4(a bit less than 4) ≈ 16 + (a bit less than 16) ≈ 32.
16 - 4√15 = 16 - 4(a bit less than 4) ≈ 16 - (a bit less than 16) ≈ 0.5.
The expression becomes:
(√32 + √0.5)².
Since (a + b)² = a² + b² + 2ab, we get:
(√32 + √0.5)²
= 32 + 0.5 + 2(√32)(√0.5)
≈ 32 + 0.5 + 2√16
= 32 + 0.5 + 8
= 40.5.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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