Find the smallest number by which the following number must be multiplied so as to get a perfect square.648

Given :

The given number is 648.

To do :

We have to find the number to be multiplied by 648 to make it a perfect square.

Solution :

The prime factorization of 648 is as follows

Prime factors of 648 $= 2\times2\times2\times3\times3\times3\times3 = 2\times(2\times2)\times(3\times3)\times(3\times3)$ 

The smallest number it needs to be multiplied to make it a perfect square is 2.

So for 648 to be a perfect square, the smallest number to be multiplied is 2.

$648\times2 = (2\times2)\times(2\times2)\times(3\times3)\times(3\times3)$

$1296 = (2\times2\times3\times3)^2$

 $1296 = (36)^2$.

Therefore, the smallest number it needs to be multiplied to make it a perfect square is 2.

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Updated on: 10-Oct-2022

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