Simplify cube root of fifth root of 27

$\sqrt[3]{\sqrt[5]{27}}$

Step 1

Rewrite $\sqrt[3]{\sqrt[5]{27}}$ as $\sqrt[15]{27}$ .

$\sqrt[15]{27}$

Step 2

Rewrite $27$ as $3^{3}$ .

$\sqrt[15]{3^{3}}$

Step 3

Rewrite $\sqrt[15]{3^{3}}$ as $\sqrt[5]{\sqrt[3]{3^{3}}}$ .

$\sqrt[5]{\sqrt[3]{3^{3}}}$

Step 4

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

$\sqrt[5]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{3}$

Decimal Form:

$1.24573093 \dots$