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If the square root of the product of two positive integers is 14, whic

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Carcass
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If the square root of the product of two positive integers is 14, whic [#permalink] New post   22 Jun 2021, 08:27
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If the square root of the product of two positive integers is 14, which can be the sum of the two integers?

Indicate all such sums.

(A) 35
(B) 53
(C) 84
(D) 100
(E) 197
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A,B,D,E
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Re: If the square root of the product of two positive integers is 14, whic [#permalink] New post   22 Jun 2021, 10:32
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Carcass wrote:
If the square root of the product of two positive integers is 14, which can be the sum of the two integers?

Indicate all such sums.

(A) 35
(B) 53
(C) 84
(D) 100
(E) 197


Let the positive integers be \(x\) and \(y\)
So, \(\sqrt{xy} = 14\)
i.e. \(xy = 196\)

Factorize \(196 = (2)(2)(7)(7)\)
(1) + (2)(2)(7)(7) = 197
(2) + (2)(7)(7) = 100
(2)(2) + (7)(7) = 53
(2)(2)(7) + (7) = 35

Hence, option A, B, D, and E
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Re: If the square root of the product of two positive integers is 14, whic [#permalink]
22 Jun 2021, 10:32
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