Simplify square root of 6/7

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

Rewrite $\sqrt{\frac{6}{7}}$ as $\frac{\sqrt{6}}{\sqrt{7}}$ .

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

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

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

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{6}}{\sqrt{7}}$ and $\frac{\sqrt{7}}{\sqrt{7}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $1$ by $1$ .

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

Evaluate the exponent.

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

Simplify the numerator.

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Combine using the product rule for radicals.

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

Multiply $6$ by $7$ .

$\frac{\sqrt{42}}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{42}}{7}$

Decimal Form:

$0.92582009 \dots$

Simplify square root of 6/7

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