SOLUTION: Hi Find the smallest value of x such that 1125x is a perfect square. Hence find the value of the square root of 1125x. Thanks

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Question 1152651: Hi
Find the smallest value of x such that 1125x is a perfect square.
Hence find the value of the square root of 1125x.
Thanks
Found 2 solutions by rothauserc, MathTherapy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
Consider the factors of 1125, looking for the largest perfect square which is a factor
:
1,3,5,9,15,25,45,75,125,225,375,1125
:
We see that 225 * 5 = 1125, therefore
:
1125x = 5 * 225 * x
:
if x = 5, we know that 1125 * 5 = 5625 and square root(5625) = 75, therefore
:
75^2 = 5625 is a perfect square
:
We know that 1125 * 1 is not a perfect square so
:
I submit that x = 5 is the smallest whole number when multiplied by 1125 yields a perfect square
:
I will leave it to you to check 2, 3, 4
:
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

Hi
Find the smallest value of x such that 1125x is a perfect square.
Hence find the value of the square root of 1125x.
Thanks 


For the above to be a PERFECT SQUARE, the FACTORS must ALL have EVEN exponents.

32 already has an EVEN exponent, but 53 needs to have the NEXT EVEN exponent, which is 4.

We then get the following: 

This means that the SMALLEST value for x is 5, and the  

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