how do you find the least positive integer n such that (2^5)*3*(5^2)*(7^3)*n = a perfect square? I don't really know where to begin on this one. Is there a mechanical process for determining whether or not a large number is a perfect square? thanks
how do you find the least positive integer n such that (2^5)*3*(5^2)*(7^3)*n = a perfect square? I don't really know where to begin on this one. Is there a mechanical process for determining whether or not a large number is a perfect square? thanks
Hello,
A perfect square is the product of perfect square, that is to say numbers put to an even power.
Here, 2^5 has to be multiplied by 2 to make an even power, and thus a perfect square.
3=3^1 has to be multiplied by 3 to make an even power, and thus a perfect square.
5^2 is already a perfect square
7^3 has to be multiplied by 7 to make an even power, and thus a perfect square.
n=2x3x7