# How do you simplify root5(6)+5root5(6)?

Jul 19, 2016

Start by noticing a chance to use the Distributive Property lurking in there, and them just combine terms.

#### Explanation:

$\sqrt[5]{6} + 5 \sqrt[5]{6}$
$= 1 \sqrt[5]{6} + 5 \sqrt[5]{6}$'cause 1 times anything is still just as anything
$= \left(1 + 5\right) \sqrt[5]{6}$distributive property applied
$= 6 \sqrt[5]{6}$
$= 6 \cdot {6}^{\frac{1}{5}}$
$= {6}^{1} \cdot {6}^{\frac{1}{5}}$
$= {6}^{\frac{6}{5}} = {6}^{1.2}$

If that radical is itself a bit noisy to look at, and you happen to notice that it's exactly the same radical in two places, try replacing that noisy $\sqrt[5]{6}$ with $x$ first and see if the distributive property usage becomes more obvious, then plug the $\sqrt[5]{6}$ back in and keep going.

IAC, whether and how far you take it past that depends on what "simplify" means to you at the moment.