Precalculus Examples

$\sqrt{\sqrt[3]{11 a^{7} b}}$

Step 1

Rewrite $11 a^{7} b$ as ${(a^{2})}^{3} \cdot (11 a b)$ .

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Step 1.1

Factor out $a^{6}$ .

$\sqrt{\sqrt[3]{11 (a^{6} a) b}}$

Step 1.2

Rewrite $a^{6}$ as ${(a^{2})}^{3}$ .

$\sqrt{\sqrt[3]{11 ({(a^{2})}^{3} a) b}}$

Step 1.3

Reorder $11$ and ${(a^{2})}^{3}$ .

$\sqrt{\sqrt[3]{{(a^{2})}^{3} \cdot 11 a b}}$

Step 1.4

Add parentheses.

$\sqrt{\sqrt[3]{{(a^{2})}^{3} \cdot 11 (a b)}}$

Step 1.5

Add parentheses.

$\sqrt{\sqrt[3]{{(a^{2})}^{3} \cdot (11 a b)}}$

Step 2

Pull terms out from under the radical.

$\sqrt{a^{2} \sqrt[3]{11 a b}}$

Step 3

Pull terms out from under the radical.

$a \sqrt{\sqrt[3]{11 a b}}$

Step 4

Rewrite $\sqrt{\sqrt[3]{11 a b}}$ as $\sqrt[6]{11 a b}$ .

$a \sqrt[6]{11 a b}$