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A perfect square is a positive integer which when square roo

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A perfect square is a positive integer which when square roo [#permalink] New post 16 Apr 2019, 00:41
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A perfect square is a positive integer which when square rooted results in an integer. If \(N = 3^4 * 5^3 * 7\), then what is the biggest perfect square that is a factor of \(N\)?

(A) \(3^2\)

(B) \(5^2\)

(C) \(9^2\)

(D) \((9 * 5)^2\)

(E) \((3 * 5 * 7)^2\)
[Reveal] Spoiler: OA

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Re: A perfect square is a positive integer which when square roo [#permalink] New post 21 Apr 2019, 05:19
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First notice that all the options are a perfect square. However we need the biggest among them. It can be seen easily that A<B<C<D therefore we can eliminate A, B and C. Now among D and E, D is bigger so it is the answer. Since both are square of some numbers in the bracket we can only compare the expression inside the bracket
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Re: A perfect square is a positive integer which when square roo [#permalink] New post 06 Aug 2019, 18:41
Carcass wrote:
A perfect square is a positive integer which when square rooted results in an integer. If \(N = 3^4 * 5^3 * 7\), then what is the biggest perfect square that is a factor of \(N\)?

(A) \(3^2\)

(B) \(5^2\)

(C) \(9^2\)

(D) \((9 * 5)^2\)

(E) \((3 * 5 * 7)^2\)



need explanation

Last edited by huda on 07 Aug 2019, 01:47, edited 6 times in total.
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Re: A perfect square is a positive integer which when square roo [#permalink] New post 14 Aug 2019, 02:27
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Precisely, what did you not get sir in the explanation above ??


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Re: A perfect square is a positive integer which when square roo [#permalink] New post 15 Aug 2019, 11:28
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Carcass wrote:
Precisely, what did you not get sir in the explanation above ??


Regards


later I got it but forgot to mention. Thanks for the concern.
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Re: A perfect square is a positive integer which when square roo [#permalink] New post 16 Aug 2019, 03:00
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Convert the options to prime factors

(A) \(3^2\)

(B) \(5^2\)

(C) \(3^4\)

(D) \(3^4 * 5^2\)

(E) \((3 * 5 * 7)^2\)

D is clearly the biggest factor of N
Re: A perfect square is a positive integer which when square roo   [#permalink] 16 Aug 2019, 03:00
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