Find the smallest number by which 2400 is to be multiplied to get a perfect square and also find the square root of the resulting number.

Given, a number as 2400. We need to find out a number which if multiplied by the given number we should get a perfect square.

To find out square root of the resulting number

Step 1: Resolve 2400 into prime factors

We get, 3 × 2 × 5 × 2 × 5 × 2 × 2 × 2

Step 2: Pair the factors obtained

⇒ (2 × 2) × (5 × 5) × (2 × 2) × 3 × 2

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

Here, 2,5 are in pairs and 3,2 are alone.

So, we must multiply the given number by 3 × 2 to get a perfect square.

⇒ 2400 × 3 × 2 = 2400 × 6 = 14400.

Step 4: The resulting number obtained is 14400

Square root is found out using common factors

⇒ = )

= 5 × 2 × 3 × 2 × 2

= 120

Hence, 6 should be multiplied to the given number “2400” to make it perfect square. The square root of the resulting number is 120.