Smallest number divided to get perfect square

Let’s do this by examples

Question

Finds the smallest number divided to 32 to get a perfect square.

Since 2 does not occur in pairs,

we divide by 2 to make it a pair

So, our number becomes

  32 × 1/2 = 2 × 2 × 2 × 2 × 2 × 1/2

Now, it becomes a perfect square.

So, we divide 32 by 2 to make it a perfect square

Question

Finds the smallest number divided to 90 to get a perfect square.

Here,

2 & 5 do not occur in pairs

So, we divide by 2 and 5 to make pairs

So, our number becomes

   90 × 1/2 × 1/ 5 = 2 × 3 × 3 × 5 × 1/2 × 1/5

Now, it becomes a perfect square.

So, we divide 90 by 2 × 5

i.e. 10  to make it a perfect square

Question

Finds the smallest number divided to 120 to get a perfect square.

Here,

2, 3 & 5 do not occur in pairs

So, we divide by 2, 3 and 5 to make pairs

So, our number becomes

Now, it becomes a perfect square.

So, we divide 120 by 2 × 3 × 5

i.e. 30  to make it a perfect square