Question

what number has its square 256/400?

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

Let the number be x.

x² =
$\frac{256}{400}$

$x = \sqrt{ \frac{256}{400} }$


We have to do the prime factorization of 256 and 400.


Prime factorization of 256.

$2 \: \: 256 \\ 2 \: \: 128 \\ 2 \: \: 64 \\ 2 \: \: 32 \\ 2 \: \: 16 \\ 2 \: \: 8 \\ 2 \: \: 4 \\ 2 \: \: 2 \\ \: \: \: \: 1$


Prime factorization of 256 = 16 × 16



Prime factorization of 400.

$2 \: \: 400 \\ 2 \: \: 200 \\ 2 \: \: 100 \\ 2 \: \: 50 \\ 5 \: \: 25 \\ 5 \: \: 5 \\ \: \: \: \: 1$


Prime factorization of 400= 20 × 20


$x = \sqrt{ \frac{16 \times 16}{20 \times 20} }$

$x = \frac{16}{20}$


HOPE IT HELPS YOU..

REGARDS
@sunita

Answer 2

Heya !!!

This is your answer.

Given :-
256/400.

You asked that which number has 256/400 has as its square.

We know that it will be its square root....

Hence square root of 256/400.....

$\sqrt{ \frac{256}{400} } \\ = \frac{ \sqrt{256} }{ \sqrt{400} } \\ = \frac{ \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 5} } \\ = \frac{2 \times 2 \times 2 \times 2}{2 \times 2 \times 5} \\ = \frac{16}{20}$
Hence the required number is 16/20.

Hope it helps