Question

Square root of 256 = .

• A. 14
• B. 15
• C. 16
• D. 12

Answer 1

The correct option is C 16

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

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