[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
If A =810+41084+411
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\(A=\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}=\sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}}=\sqrt{\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}}=\sqrt{2^8}=2^4=16\)
Then, (A + 4)^2 = (16 + 4)^2 = 20^2 = 400.
Therefore, C is the answer.
Answer: C
\(A=\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}=\sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}}=\sqrt{\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}}=\sqrt{2^8}=2^4=16\)
Then, (A + 4)^2 = (16 + 4)^2 = 20^2 = 400.
Therefore, C is the answer.
Answer: C
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