Simplify fourth root of cube root of 64

$\sqrt[4]{\sqrt[3]{64}}$

Step 1

Rewrite $64$ as $4^{3}$ .

$\sqrt[4]{\sqrt[3]{4^{3}}}$

Step 2

Pull terms out from under the radical, assuming real numbers.

$\sqrt[4]{4}$

Step 3

Rewrite $4$ as $2^{2}$ .

$\sqrt[4]{2^{2}}$

Step 4

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$\sqrt{\sqrt{2^{2}}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$