Algebra Examples

$\sqrt{6} \cdot \sqrt[4]{6}$

Step 1

Multiply $\sqrt{6} \sqrt[4]{6}$ .

Tap for more steps...

Step 1.1

Rewrite the expression using the least common index of $4$ .

Tap for more steps...

Step 1.1.1

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

$6^{\frac{1}{2}} \sqrt[4]{6}$

Step 1.1.2

Rewrite $6^{\frac{1}{2}}$ as $6^{\frac{2}{4}}$ .

$6^{\frac{2}{4}} \sqrt[4]{6}$

Step 1.1.3

Rewrite $6^{\frac{2}{4}}$ as $\sqrt[4]{6^{2}}$ .

$\sqrt[4]{6^{2}} \sqrt[4]{6}$

Step 1.2

Combine using the product rule for radicals.

$\sqrt[4]{6^{2} \cdot 6}$

Step 1.3

Multiply $6^{2}$ by $6$ by adding the exponents.

Tap for more steps...

Step 1.3.1

Multiply $6^{2}$ by $6$ .

Tap for more steps...

Step 1.3.1.1

Raise $6$ to the power of $1$ .

$\sqrt[4]{6^{2} \cdot 6^{1}}$

Step 1.3.1.2

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

$\sqrt[4]{6^{2 + 1}}$

Step 1.3.2

Add $2$ and $1$ .

$\sqrt[4]{6^{3}}$

Step 2

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

$\sqrt[4]{216}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{216}$

Decimal Form:

$3.83365862 \dots$