Question

How do you simplify `sqrt (a^5 / 2)`?

Answer 1

`sqrt (a^5 / 2)=sqrt(a^5)/sqrt2=sqrt(a^4*a)/sqrt2`

`=[sqrt(a^4)*sqrta]/sqrt2=[a^2*sqrta]/sqrt2`

Explanation:

Note that

`color(red)[sqrt(a/b)=sqrta/sqrtb]`

`sqrt (a^5 / 2)=sqrt(a^5)/sqrt2=sqrt(a^4*a)/sqrt2`

`=[sqrt(a^4)*sqrta]/sqrt2=[a^2*sqrta]/sqrt2`