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

multiple by 5 then it becomes 900

primefactorise 180 then make pairs of prime factors and the excess number to be multiplied

Answer 2

Let us factorise the number 180

180 = 2 × 2 × 3 × 3 × 5

You can see that the pair of 5 is incomplete.

So to make it a perfect square we should multiply it by 5.

And that's the smallest number.

180 × 5 = 900

which is a square of number 30.