Question

Find the square root of 256.

Answer 1

Hint: - Use the concept of factorization.

We have to find out the square root of 256 $=\sqrt{256}$

So, factors of 256 are $=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
$256=2^8..............\left(1\right)$

Now $\sqrt{256}$ is also written as ${\left(256\right)}^{{\displaystyle \frac{1}{2}}}$

Therefore from equation 1
${\left(256\right)}^{{\displaystyle \frac{1}{2}}}={\left(2^8\right)}^{{\displaystyle \frac{1}{2}}}=2^{{\displaystyle \frac{8}{2}}}=2^4=16$
So, it is clear that the square root of 256 is 16.

So, 16 is the required square root.

Note: - In such types of questions the key concept is that first find out the factors of the given number, then substitute these factors in place of the original number in square root, then cancel out its square root power with the power of factors, then we will get the required square root.