Simplify the Radical Expression ( square root of 7)/( square root of 11)

$\frac{\sqrt{7}}{\sqrt{11}}$

Step 1

Multiply $\frac{\sqrt{7}}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{\sqrt{7}}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7}}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{\sqrt{7} \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{11}}{{\sqrt{11}}^{1} \sqrt{11}}$

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{11}}{{\sqrt{11}}^{1} {\sqrt{11}}^{1}}$

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

$\frac{\sqrt{7} \sqrt{11}}{{\sqrt{11}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{7} \sqrt{11}}{{\sqrt{11}}^{2}}$

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\frac{\sqrt{7} \sqrt{11}}{{(11^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{7} \sqrt{11}}{11^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{7} \sqrt{11}}{11^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{7} \sqrt{11}}{11^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{7} \sqrt{11}}{11^{1}}$

Evaluate the exponent.

$\frac{\sqrt{7} \sqrt{11}}{11}$

Step 3

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{7 \cdot 11}}{11}$

Multiply $7$ by $11$ .

$\frac{\sqrt{77}}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{77}}{11}$

Decimal Form:

$0.79772403 \dots$