Question

What is the least number which must be multiplied with 18144 to get a perfect square?

Answer 1

14 is the answer.........................

Answer 2

Given:

A  number 18144.

To Find:

The least number is to be multiplied by 18144 such that the number becomes a perfect square.

1. The given number is 18144. Express the number as the product of the prime factors.

2. Factorize the number 18144,

=> 18144 = 2 x 9072,

=> 18144 = 2 x 2 x 4536,

=> 18144 = 2 x 2 x 2 x 2268,

=> 18144 = 2 x 2 x 2 x 2 x 1134,

=> 18144 = 2 x 2 x 2 x 2 x 2 x 567.

=> 18144 = 2 x 2 x 2 x 2 x 2 x 3 x 189,

=> 18144 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 63,

=> 18144 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 21,

=> 18144 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x7,

3. For a number to be a perfect square, all the factors must be repeated an even number of times, In the given number the factors 2 and 7 are repeated only once. Hence the least number to be multiplied is 2x7.

=> The least number to be multiplied with 18144 to get a perfect square is 14.

=> The value of √(18144x14) is 504.

Therefore, the least number that is to be multiplied with 18144 to get a perfect square is 14.