Question

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Answer 1

Factorising 180,

=$180=2\times 2\times 3\times 3\times 5$
Grouping the factors in pairs we see that factor 5 is left unpaired.
$\therefore$ Multiply 180 by 5, we get the product $180\times 5=900$ Which is a perfect square
and square root of $900=2\times 3\times 5=30$