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# If x and y are perfect squares, then which one of the

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Re: If x and y are perfect squares, then which one of the [#permalink]
Option B is not clear to me....
X=a^2
Y=b^2

Therefore X*Y = (ab)^2
But, if x=4 and y=9 , then xy=25
However, if x= 4 and y = 25, then xy = 100 which is not perfect square

So, how can we rule out B?

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Re: If x and y are perfect squares, then which one of the [#permalink]
sdas wrote:
Option B is not clear to me....
X=a^2
Y=b^2

Therefore X*Y = (ab)^2
But, if x=4 and y=9 , then xy=25
However, if x= 4 and y = 25, then xy = 100 which is not perfect square

So, how can we rule out B?

If x=4 and y=9 xy =36 which is a perfect square. and xy=100 is a perfect square. its the square of 10.
for that matter , product of any two perfect squares is a perfect square. as you pointed out (ab)^2. so square root of the product is ab an integer.

4*9 or 9*25 or 16*25
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Re: If x and y are perfect squares, then which one of the [#permalink]
sdas wrote:
Option B is not clear to me....
X=a^2
Y=b^2

Therefore X*Y = (ab)^2
But, if x=4 and y=9 , then xy=25
However, if x= 4 and y = 25, then xy = 100 which is not perfect square

So, how can we rule out B?

XY = 36 = 6^2

XY for x=4 and Y = 25 is 100 = 10^2, which is a perfect square.
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Re: If x and y are perfect squares, then which one of the [#permalink]
shreya717 wrote:
If x and y are perfect squares, then which one of the following is not necessarily a perfect square?

A. x^2
B. xy
C. 4x
D. x+y
E. x^5

Seems like a straight forward problem, however the answer choices are a little confusing .

both D& E seem to be contendors for the right answer though the OA is D

D-> Because the sum of two perfect square needn't necessarily be a perfect square e.g 4+9=13, not a perfect square, however 9 & 16 = 25 which is a perfect square)
E-> Because a perfect square to the power 5 (an ODD number) cannot be a perfect square right ?

Thanks,
Shreya

If x=y=1^2=1, then each option but D is a perfect square, therefore D is NOT necessarily a perfect square.

P.S. Notice that x+y could be a perfect square for example if x=3^2=9 and y=4^2=16 --> x+y=25=5^2.
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Re: If x and y are perfect squares, then which one of the [#permalink]
Darn....I forgot perfect square of 10.
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Re: If x and y are perfect squares, then which one of the [#permalink]
Since x and y are perfect squares, we can write:
x=n^2 and y=m^2, for some integers m and n.

Let's evaluate the options now:
1. x^2 = (n^2)^2. Thus, x^2 is a perfect square (the square of n^2).
2. xy = (n^2)(m^2)= (nm)^2. Thus, xy is a perfect square (the square of xy)
3. 4x = 4(n^2)= (2n)^2. Thus, 4x is a perfect square (the square of 2n)
4. x+y= (n^2)+(m^2). This is NOT necessarily a perfect square.

Hence, we have our answer. It is D.
Re: If x and y are perfect squares, then which one of the [#permalink]
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