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 
<pre>{{{matrix(1,5, 1125x, "=", "3.3.5.5.5.x.", "=", 3^2 * 5^3 * x)}}}
For the above to be a PERFECT SQUARE, the FACTORS must ALL have EVEN exponents.
3<sup>2</sup> already has an EVEN exponent, but 5<sup>3</sup> needs to have the NEXT EVEN exponent, which is 4.
We then get the following: {{{matrix(1,7, 3^2 * 5^3 * 5, "=", 3^2 * 5^4, "=", 9(625), "=", "5,625")}}}
This means that the SMALLEST value for x is 5, and the {{{highlight_green(matrix(1,11, sqrt(1125x), or, sqrt("1,125(5)"), "=", sqrt(3^2 * 5^4), "=", 3(5^2), "=", 3(25), "=", 75))}}}