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# The integer v is greater than 1. If v is the square of an integer, whi

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Math Expert
Joined: 02 Sep 2009
Posts: 59125
The integer v is greater than 1. If v is the square of an integer, whi  [#permalink]

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23 May 2019, 01:47
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Difficulty:

75% (hard)

Question Stats:

33% (01:49) correct 67% (02:20) wrong based on 30 sessions

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The integer v is greater than 1. If v is the square of an integer, which of the following numbers must also be the square of an integer?

I. $$81v$$

II. $$25v + 10 \sqrt{v} + 1$$

III. $$4v^2 + 4 \sqrt{v} + 1$$

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

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The integer v is greater than 1. If v is the square of an integer, whi  [#permalink]

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23 May 2019, 02:15
Bunuel wrote:
The integer v is greater than 1. If v is the square of an integer, which of the following numbers must also be the square of an integer?

I. $$81v$$

II. $$25v + 10 \sqrt{v} + 1$$

III. $$4v^2 + 4 \sqrt{v} + 1$$

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

I is square of integer 9 * root(v), v is a square of an integer so root(v) will also give an integer.
II square of integer {5root(v) + 1}
III NOT square of integer {2root(v) + 1}. The expression is definitely an Integer but not sure whether square of an integer or not.

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The integer v is greater than 1. If v is the square of an integer, whi   [#permalink] 23 May 2019, 02:15
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