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A perfect square is a positive integer which when square rooted result

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A perfect square is a positive integer which when square rooted result  [#permalink]

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New post 10 Apr 2019, 01:07
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A
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D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:15) correct 37% (01:25) wrong based on 41 sessions

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A perfect square is a positive integer which when square rooted result  [#permalink]

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New post Updated on: 11 Apr 2019, 00:10
Bunuel 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


\(N = 3^4*5^3*7\)
perfect squre = 3^2*5*√35 ; 45
so biggest factor would be (9*5)^2
IMO D
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Originally posted by Archit3110 on 10 Apr 2019, 03:25.
Last edited by Archit3110 on 11 Apr 2019, 00:10, edited 1 time in total.
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A perfect square is a positive integer which when square rooted result  [#permalink]

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New post 10 Apr 2019, 06:09
As we can see Square root of 3^4*5^2 will be 3^2*5 or 9*5
so for N=3^4∗5^3∗7, (9*5)^2 will be biggest perfect square factor.
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Re: A perfect square is a positive integer which when square rooted result  [#permalink]

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New post 13 Apr 2019, 18:37
Bunuel 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


Recall that a perfect square always has prime factors whose exponents are even numbers. So the perfect squares that are factors of N are 3^4 and 5^2. Therefore, the biggest perfect square that is a factor of N is 3^4 x 5^2 = (3^2 x 5)^2 = (9 x 5)^2.

Answer: D
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Re: A perfect square is a positive integer which when square rooted result   [#permalink] 13 Apr 2019, 18:37
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