Question

Which expression is equivalent to sqrt2x^5/18 ? Assume x>0.

Answer 1

`(x^(2) √(x) )/(3)`

Explanation:

first off rt(2x^5) can be simplified as x^2 rt(2x) because we can break up x^5 into x^4 * x. x^4 is a perfect square so factor out a x^2.

the denominator
`√(18)` can be written as
`3√(2)` since the factors of 18 involve a perfect square of 9. 9*2 is 18 so factor out a 3.

the whole fraction :

`(x^(2) √(2x) )/(3√(2) )`

cancel out the
`√(2)` and you are left with
`(x^(2) √(x) )/(3)`