Algebra Examples

$\sqrt[3]{8} \div \sqrt{6}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[3]{8}}{\sqrt{6}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Pull terms out from under the radical.

$\frac{2}{\sqrt{6}}$

Step 3

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{2}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{2 \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Step 4.2

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Step 4.3

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Step 4.4

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

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{2}}$

Step 4.6

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 4.6.1

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

$\frac{2 \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{6}}{6^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.6.4.1

Cancel the common factor.

$\frac{2 \sqrt{6}}{6^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{2 \sqrt{6}}{6^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{2 \sqrt{6}}{6}$

Step 5

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 5.1

Factor $2$ out of $2 \sqrt{6}$ .

$\frac{2 (\sqrt{6})}{6}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $2$ out of $6$ .

$\frac{2 \sqrt{6}}{2 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{2 \sqrt{6}}{2 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{\sqrt{6}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{3}$

Decimal Form:

$0.81649658 \dots$