Question

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

Answer 1

Answer

$\frac{x^{2} \sqrt{x} }{3}$

Step-by-step 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 $\sqrt{18}$ can be written as $3\sqrt{2}$ since the factors of 18 involve a perfect square of 9. 9*2 is 18 so factor out a 3.

the whole fraction :

$\frac{x^{2} \sqrt{2x} }{3\sqrt{2} }$

cancel out the $\sqrt{2}$ and you are left with $\frac{x^{2} \sqrt{x} }{3}$