Simplify square root of 6/7* square root of 1/3

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

Combine using the product rule for radicals.

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

Multiply $\frac{6}{7}$ by $\frac{1}{3}$ .

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

Reduce the expression $\frac{6}{7 \cdot 3}$ by cancelling the common factors.

Factor $3$ out of $6$ .

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

Factor $3$ out of $7 \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $\frac{\sqrt{2}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{2}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{2}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

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

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

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

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

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

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

$\frac{\sqrt{2} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 7}}{7}$

Multiply $2$ by $7$ .

$\frac{\sqrt{14}}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{14}}{7}$

Decimal Form:

$0.53452248 \dots$

Simplify square root of 6/7* square root of 1/3

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