Basic Math Examples

$\sqrt[6]{3} \cdot \sqrt{6}$

Step 1

Rewrite the expression using the least common index of $6$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\sqrt[6]{3} \cdot 6^{\frac{1}{2}}$

Step 1.2

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{3}{6}}$ .

$\sqrt[6]{3} \cdot 6^{\frac{3}{6}}$

Step 1.3

Rewrite $6^{\frac{3}{6}}$ as $\sqrt[6]{6^{3}}$ .

$\sqrt[6]{3} \sqrt[6]{6^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[6]{3 \cdot 6^{3}}$

Step 3

Raise $6$ to the power of $3$ .

$\sqrt[6]{3 \cdot 216}$

Step 4

Multiply $3$ by $216$ .

$\sqrt[6]{648}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{648}$

Decimal Form:

$2.94168275 \dots$