Simplify square root of 7/6

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

Step 1

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

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $7$ by $6$ .

$\frac{\sqrt{42}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{42}}{6}$

Decimal Form:

$1.08012344 \dots$