Find the smallest number by which 10,368 should be multiplied to make it a perfect square.

Given: 10,368

To find: Here we have to find the smallest number by which 10,368 should be multiplied to make it a perfect square.

Solution:

The prime factors of 10368 are:

10368 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 3

10368 = 2 $\times$ (2⁶ $\times$ 3⁴)

Perfect squares have an even number of each prime factor.

We can make a perfect square by multiplying by 2.

Now,

10368 $\times$ 2 = 20736

And,

20736 = 144²  

So, the smallest number by which 10,368 should be multiplied to make it a perfect square is 2.