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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
A perfect square is a positive integer which when square rooted result  [#permalink]

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10 Apr 2019, 01:07
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:19) correct 37% (01:27) wrong based on 78 sessions

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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

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

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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

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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Joined: 06 Apr 2019
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A perfect square is a positive integer which when square rooted result  [#permalink]

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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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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.

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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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