Basic Math Examples

$\sqrt{3} (\sqrt[8]{3})$

Step 1

Multiply $\sqrt{3} (\sqrt[8]{3})$ .

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Step 1.1

Rewrite the expression using the least common index of $8$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$3^{\frac{1}{2}} \sqrt[8]{3}$

Step 1.1.2

Rewrite $3^{\frac{1}{2}}$ as $3^{\frac{4}{8}}$ .

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

Step 1.1.3

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

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Multiply $3^{4}$ by $3$ by adding the exponents.

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Step 1.3.1

Multiply $3^{4}$ by $3$ .

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Step 1.3.1.1

Raise $3$ to the power of $1$ .

$\sqrt[8]{3^{4} \cdot 3^{1}}$

Step 1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[8]{3^{4 + 1}}$

Step 1.3.2

Add $4$ and $1$ .

$\sqrt[8]{3^{5}}$

Step 2

Raise $3$ to the power of $5$ .

$\sqrt[8]{243}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[8]{243}$

Decimal Form:

$1.98701334 \dots$