Question

The square root of 256 is __.

Answer 1

Prime factorization of 256 is

$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

The square of a number contains every prime number twice.
For finding the square root, group similar prime factors in a group of two and then count them as one.

So, the square root of 256 will be $2\times 2\times 2\times 2=16$

Alternate:
$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
Make pairs of prime numbers
$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\downarrow \downarrow \downarrow \downarrow \sqrt{256}=2\times 2\times 2\times 2=16$