Question

Question #f2e51

Answer 1

`(5sqrt(2))/16`

Explanation:

You are looking for ways to split the numbers into squared values that you can 'take outside' the root

For example `25 ->5^2` so `sqrt(25)=sqrt(5^2)=5`

You can write `sqrt(25/128)` as `sqrt(25)/sqrt(128)`

If you are ever not sure about roots build a factor tree diagram (sketch) at the side of your work area. Do not forget to label it as rough work.

`sqrt(25/128)" "= "sqrt(5^2)/(sqrt(2^2xx2^2xx2^2xx2))`

`=5/(2xx2xx2xxsqrt(2)) = 5/(8sqrt(2))`

Mathematicians do not like roots in the denominator so lets get rid of it.

Multiply by 1 and you do not change the intrinsic value.

`color(green)(5/(8sqrt(2))color(red)(xx1)" "->" "5/(8sqrt(2))color(red)(xxsqrt(2)/sqrt(2))`

`" "color(green)((5sqrt(2))/(8xx2)" "=" "(5sqrt(2))/16)`