How do you simplify $64^{\frac{1}{4}}$ $64^(1/4)$ ?

Question

28946 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-19T10:28:25

$2 \sqrt{2}$ $2sqrt2$

$64 = 2^{6}$ $64=2^6$
So it can be written as
${(2^{6})}^{\frac{1}{4}}$ $(2^6)^(1/4)$
= $2^{\frac{3}{2}} = 2 \sqrt{2}$ $2^(3/2)=2sqrt2$

Answer 2 · 2016-06-19T11:14:40

$2 \sqrt{2}$ $2sqrt2$

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

$\sqrt[4]{x} = \sqrt{\sqrt{x}}$ $root(4)x =sqrt(sqrtx)$

$\sqrt[4]{64} = \sqrt{\sqrt{64}} = \sqrt{8}$ $root(4)64 = sqrt(sqrt64) = sqrt8$

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

$\sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2}$ $sqrt8 = sqrt(4 xx 2) = 2sqrt2$

How do you simplify 641464^(1/4)?