Question

how is √200 converted into 10√2

Answer 1

Hello,

This is easy to do by prime Factorization.

First we will factorise 200
So,
It comes that

200 = 2 * 2*5 *2 *5

Now ,
This means that
$\sqrt{200} = \sqrt{2 \times 2 \times 2 \times 5 \times 5}$
Now,
We know that anything inside the root can come out when it is twice.

So,
5 and 2 are two times inside root
So,
This will come out as one.

So,
$\sqrt{2 \times 2 \times 2 \times 5 \times 5} = 5 \times 2 \sqrt{2} \\ = 10 \sqrt{2}$
This is how
$\sqrt{200} = 10 \sqrt{2}$


Hope this will be helping you