Linear Algebra Examples

$\frac{\sqrt[5]{32} + 3 \sqrt[3]{8}}{\sqrt[4]{81}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $32$ as $2^{5}$ .

$\frac{\sqrt[5]{2^{5}} + 3 \sqrt[3]{8}}{\sqrt[4]{81}}$

Step 1.2

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

$\frac{2 + 3 \sqrt[3]{8}}{\sqrt[4]{81}}$

Step 1.3

Rewrite $8$ as $2^{3}$ .

$\frac{2 + 3 \sqrt[3]{2^{3}}}{\sqrt[4]{81}}$

Step 1.4

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

$\frac{2 + 3 \cdot 2}{\sqrt[4]{81}}$

Step 1.5

Multiply $3$ by $2$ .

$\frac{2 + 6}{\sqrt[4]{81}}$

Step 1.6

Add $2$ and $6$ .

$\frac{8}{\sqrt[4]{81}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $81$ as $3^{4}$ .

$\frac{8}{\sqrt[4]{3^{4}}}$

Step 2.2

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

$\frac{8}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$