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If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2?

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Bunuel
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If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2? [#permalink] New post   30 May 2023, 04:30
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If \(A =\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}\) , what is \((A + 4)^2\)?

A. \(20\)

B. \(225\)

C. \(400\)

D. \(500\)

E. \(900\)
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$!vakumar.m
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Re: If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2? [#permalink] New post   30 May 2023, 09:55
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A can be reduced to value of 16 (write all the terms inside square root in terms of powers of 2 and then cancel out common values from numerator and denominator)
thereafter (A+4)^2 = 400
Answer C
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Re: If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2? [#permalink] New post   22 Nov 2023, 08:20
Can anyone elaborate?
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If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2? [#permalink] New post   22 Nov 2023, 08:32
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Robiacca wrote:
Can anyone elaborate?

8^10 = (\(2^3\))^10 = 2^30
4^10 = (\(2^2\))^10 = 2^20
So 8^10 + 4^10 = 2^30 + 2^20 = 2^20(2^10 + 1)

Similarly, denominator can be simplified to 2^12(2^10 + 1)

So numerator/ denominator = 2^20(2^10 + 1) / 2^12(2^10 + 1) = 2^20 / 2^12 = \(2^8\)
and A = sqrt of \(2^8 = 2^4 = 16.\)
thereafter (A+4)^2 = 400

Hope this helps
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If A = (8^10 + 4^10)/(8^4 + 4^11), what is (A + 4)2? [#permalink]
22 Nov 2023, 08:32
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