Question

find the smallest number by which 2592,be multiplied so that the product is a perfect square

Answer 1

2592 = 2×2×2×2×2×3×3×3×3
now,
√2592 = √2×2×2×2×2×3×3×3×3 = 2×2×3×3√2 = 36√2
as √2 is left so the number 2592 should be multiplied with 2 to get a perfect square.

Answer 2

Answer:

The smallest number is 2 which has to be multiplied.

Step-by-step explanation:

Given : Number 2592

To find : The smallest number by which 2592,be multiplied so that the product is a perfect square?

Solution :

First we factor the given number,

$2592 = 2\times2\times2\times2\times2\times3\times3\times3\times3$

or $2592 = 36\sqrt 2$

This means we have to multiply 2 so that we get a perfect square.

So, $2592\times 2=5184$

$\sqrt{5184}=72$

Therefore, The smallest number is 2 which has to be multiplied.