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If A =810+41084+411

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by Max@Math Revolution » Mon Feb 17, 2020 12:26 am
[GMAT math practice question]

If \(A=\sqrt{\frac{^{8^{10}+4^{10}}}{8^4+4^{11}}}\) , what is \(\left(A+4\right)^2\) ?

A. 20
B. 225
C. 400
D. 500
E. 900
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Re: If A =810+41084+411

by Max@Math Revolution » Wed Feb 19, 2020 1:10 am
=>
\(A=\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}=\sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}}=\sqrt{\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}}=\sqrt{2^8}=2^4=16\)

Then, (A + 4)^2 = (16 + 4)^2 = 20^2 = 400.

Therefore, C is the answer.
Answer: C
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