Question

IV. Solve the following. 1. Find the smallest number by which 2048 must be multiplied to get a perfect square. Also find the square root of the perfect square so obtained.​

Answer 1

Let's find the factors of 2048

2048

2*2*2*2*2*2*2*2*2* 2*2

(2*2) * (2*2) * (2*2) * (2*2) * (2*2) * 2

Since (2*2) is a perfect square, we need to multiply 2048 by 2 so that it becomes a perfect square.

2048 * 2

(2*2) * (2*2) * (2*2) * (2*2) * (2*2) * (2*2)

{(2*2) * (2*2) * (2*2) } * {(2*2) * (2*2) * (2*2) }

{(2*2) * (2*2) * (2*2) } ^ 2

(4*4*4) ^ 2

64 ^ 2

Hence, 64 is the square root of the number which is obtained by multiplying 2048 by 2.

Hope you understand