Simplify the Radical Expression ( square root of 3)/(6 square root of 7)

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

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

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

Combine and simplify the denominator.

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

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

Move $\sqrt{7}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $3$ by $7$ .

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

Multiply $6$ by $7$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.10910894 \dots$