# How do you simplify 64^(1/4)?

Jun 19, 2016

$2 \sqrt{2}$

#### Explanation:

$64 = {2}^{6}$
So it can be written as
${\left({2}^{6}\right)}^{\frac{1}{4}}$
=${2}^{\frac{3}{2}} = 2 \sqrt{2}$

Jun 19, 2016

$2 \sqrt{2}$

#### Explanation:

One should remember that finding a fourth root is the same as finding the square root twice.

$\sqrt[4]{x} = \sqrt{\sqrt{x}}$

$\sqrt[4]{64} = \sqrt{\sqrt{64}} = \sqrt{8}$

However 8 is not a perfect square so it does not have an exact square root.

$\sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2}$