Algebra Examples

$\frac{\sqrt{3}}{6 \sqrt{7}}$

Step 1

Multiply $\frac{\sqrt{3}}{6 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{3}}{6 \sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{\sqrt{3}}{6 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{3} \sqrt{7}}{6 \sqrt{7} \sqrt{7}}$

Step 2.2

Move $\sqrt{7}$ .

$\frac{\sqrt{3} \sqrt{7}}{6 (\sqrt{7} \sqrt{7})}$

Step 2.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{7}}{6 ({\sqrt{7}}^{1} \sqrt{7})}$

Step 2.4

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{7}}{6 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}$

Step 2.5

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

$\frac{\sqrt{3} \sqrt{7}}{6 {\sqrt{7}}^{1 + 1}}$

Step 2.6

Add $1$ and $1$ .

$\frac{\sqrt{3} \sqrt{7}}{6 {\sqrt{7}}^{2}}$

Step 2.7

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{\sqrt{3} \sqrt{7}}{6 {(7^{\frac{1}{2}})}^{2}}$

Step 2.7.2

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

$\frac{\sqrt{3} \sqrt{7}}{6 \cdot 7^{\frac{1}{2} \cdot 2}}$

Step 2.7.3

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

$\frac{\sqrt{3} \sqrt{7}}{6 \cdot 7^{\frac{2}{2}}}$

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

$\frac{\sqrt{3} \sqrt{7}}{6 \cdot 7^{\frac{2}{2}}}$

Step 2.7.4.2

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{7}}{6 \cdot 7^{1}}$

Step 2.7.5

Evaluate the exponent.

$\frac{\sqrt{3} \sqrt{7}}{6 \cdot 7}$

Step 3

Simplify the numerator.

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Step 3.1

Combine using the product rule for radicals.

$\frac{\sqrt{3 \cdot 7}}{6 \cdot 7}$

Step 3.2

Multiply $3$ by $7$ .

$\frac{\sqrt{21}}{6 \cdot 7}$

Step 4

Multiply $6$ by $7$ .

$\frac{\sqrt{21}}{42}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{21}}{42}$

Decimal Form:

$0.10910894 \dots$