Question

what is the smallest number by which 24000 may be divided so that the product is a perfect cube

Answer 1

Answer:

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 x 2 x 5 x 2 x 5 x 2 x 2 x 2

Step 2: Pair the factors obtained

(2 x 2) x (5 × 5) x (2 x 2) x 3 x 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 x 2 to get a perfect square.

→ 2400 x 3 x 2 = 2400 x 6 = 14400.

Step 4: The resulting number obtained 14400 Square root is found out using common factors

= 5 x 2 x 3 x 2 x 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.