# How do you simplify 3root4(128)?

May 29, 2017

$= 6 \sqrt[4]{{2}^{3}}$

#### Explanation:

When you are working with roots, write the radicand as the product of prime factors. That way you know what you are working with.

$3 \sqrt[4]{128} = 3 \sqrt[4]{{2}^{7}}$

Write as $4 t h$ powers if possible:

$3 \sqrt[4]{{2}^{7}} = 3 \sqrt[4]{{2}^{4} \times {2}^{3}}$

Now find any roots possible:

$= 3 \times 2 \sqrt[4]{{2}^{3}}$

$= 6 \sqrt[4]{{2}^{3}}$