Question

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.

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

Alternate: $256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Make pairs of prime numbers

$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\downarrow \downarrow \downarrow \downarrow \sqrt{256}=2\times 2\times 2\times 2=16$