Find the smallest number by which 3645 must be multiplied to get a perfect square.

Given, a number as 3645. We need to find out a number which if multiplied by the given number we should get a perfect square.

Step 1: Resolve 3645 into prime factors

We get, 5 × 9 × 9 × 3 × 3

Step 2: Pair the factors obtained

⇒ (9 × 9) × (3 × 3) × 5

Step 3: multiply the number with the factor which is alone.

Here, 9,3 are in pair and 5 is alone.

So,we must multiply the given number by 5 to get a perfect square.

⇒ 3645 × 5 = 18225.

Hence, 5 should be multiplied to the given number “3645” to make it perfect square.