Pre-Algebra Examples

$\frac{7 \sqrt{3}}{2 \sqrt{11}}$

Step 1

Multiply $\frac{7 \sqrt{3}}{2 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{7 \sqrt{3}}{2 \sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{7 \sqrt{3}}{2 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{7 \sqrt{3} \sqrt{11}}{2 \sqrt{11} \sqrt{11}}$

Step 2.2

Move $\sqrt{11}$ .

$\frac{7 \sqrt{3} \sqrt{11}}{2 (\sqrt{11} \sqrt{11})}$

Step 2.3

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 ({\sqrt{11}}^{1} \sqrt{11})}$

Step 2.4

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 ({\sqrt{11}}^{1} {\sqrt{11}}^{1})}$

Step 2.5

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 {\sqrt{11}}^{1 + 1}}$

Step 2.6

Add $1$ and $1$ .

$\frac{7 \sqrt{3} \sqrt{11}}{2 {\sqrt{11}}^{2}}$

Step 2.7

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

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Step 2.7.1

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 {(11^{\frac{1}{2}})}^{2}}$

Step 2.7.2

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 \cdot 11^{\frac{1}{2} \cdot 2}}$

Step 2.7.3

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

$\frac{7 \sqrt{3} \sqrt{11}}{2 \cdot 11^{\frac{2}{2}}}$

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

$\frac{7 \sqrt{3} \sqrt{11}}{2 \cdot 11^{\frac{2}{2}}}$

Step 2.7.4.2

Rewrite the expression.

$\frac{7 \sqrt{3} \sqrt{11}}{2 \cdot 11^{1}}$

Step 2.7.5

Evaluate the exponent.

$\frac{7 \sqrt{3} \sqrt{11}}{2 \cdot 11}$

Step 3

Simplify the numerator.

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Step 3.1

Combine using the product rule for radicals.

$\frac{7 \sqrt{11 \cdot 3}}{2 \cdot 11}$

Step 3.2

Multiply $11$ by $3$ .

$\frac{7 \sqrt{33}}{2 \cdot 11}$

Step 4

Multiply $2$ by $11$ .

$\frac{7 \sqrt{33}}{22}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7 \sqrt{33}}{22}$

Decimal Form:

$1.82781538 \dots$