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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]  16 Apr 2019, 00:41
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66% (00:56) correct 33% (00:00) wrong based on 12 sessions
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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Director
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Re: A perfect square is a positive integer which when square roo [#permalink]  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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Director
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Re: A perfect square is a positive integer which when square roo [#permalink]  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
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Last edited by huda on 07 Aug 2019, 01:47, edited 6 times in total.
Founder
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Re: A perfect square is a positive integer which when square roo [#permalink]  14 Aug 2019, 02:27
Expert's post
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]  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]  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
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Re: A perfect square is a positive integer which when square roo [#permalink]  19 Aug 2019, 08:39
I keep wondering isnt 3*5*7 sq bigger?
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Re: A perfect square is a positive integer which when square roo [#permalink]  19 Aug 2019, 10:56
Expert's post
No

Regards
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Re: A perfect square is a positive integer which when square roo   [#permalink] 19 Aug 2019, 10:56
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