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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.
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