Question

find the smasllest no. by which 1100 must be multiplied so that the product a perfect square

Answer 1

x²=1100n
let n be the smallest no.
$x ^{2} = \sqrt{1100n } \\ x ^{2} = 10 \sqrt{n \times 11 } \\ for \: this \: number \: to \: be \: a \: perfect \: square \: \\ n \: must \: be \: equal \: to \: 11$
so the least number that we must multiply to 1100 to have a perfect square is 11