# How do you simplify root3(16 )+ 3+root3(54))?

Oct 9, 2015

$5 \sqrt[3]{2} + 3$

#### Explanation:

Factor 16, down to its primes

$16 | 2$
$\textcolor{w h i t e}{0} 8 | 2$
$\textcolor{w h i t e}{0} 4 | 2$
$\textcolor{w h i t e}{0} 2 | 2$
$\textcolor{w h i t e}{0} 1 | {2}^{4}$

Factor 54, down to its primes

$54 | 2$
$27 | 3$
$\textcolor{w h i t e}{0} 9 | 3$
$\textcolor{w h i t e}{0} 3 | 3$
$\textcolor{w h i t e}{0} 1 | 2 \cdot {3}^{3}$

Subsitute these

$\sqrt[3]{{2}^{3} \cdot 2} + 3 + \sqrt[3]{2 \cdot {3}^{3}}$

Everything with an exponent that's 3 or a multiple of it can come out of the root

$2 \sqrt[3]{2} + 3 + 3 \sqrt[3]{2}$

Sum everything that has $\sqrt[3]{2}$ together

$5 \sqrt[3]{2} + 3$