Let’s do this by examples

### Finds the smallest number multiplied by 32 to get a perfect square.

Since 2 does not occur in pair,

we multiply by 2 to make it a pair

So, our number becomes

Now, it becomes a perfect square.

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

### Finds the smallest number multiplied by 90 to get a perfect square.

Here,

2 & 5 do not occur in pairs

So, we multiply by 2 and 5 to make pairs

So, our number becomes

90 ×
**
2 × 5
**
= 2 × 3 × 3 × 5 ×
**
2 ×
**
**
5
**

**
**

Now, it becomes a perfect square.

So, we multiply 90 by 2 × 5

i.e.
**
10
**
to make it a perfect square

### Finds the smallest number multiplied by 120 to get a perfect square.

Here,

2, 3 & 5 do not occur in pairs

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

So, our number becomes

120 ×
**
2
**
**
×
**
**
3 × 5
**
= 2 × 2 × 2 × 3 × 5 ×
**
2 ×
**
**
3
**
**
× 5
**

**
**

Now, it becomes a perfect square.

So, we multiply 120 by 2 × 3 × 5

i.e.
**
30
**
to make it a perfect square