Pre-Algebra Examples

$\frac{4 \sqrt{15}}{3 \sqrt{14}}$

Step 1

Multiply $\frac{4 \sqrt{15}}{3 \sqrt{14}}$ by $\frac{\sqrt{14}}{\sqrt{14}}$ .

$\frac{4 \sqrt{15}}{3 \sqrt{14}} \cdot \frac{\sqrt{14}}{\sqrt{14}}$

Step 2

Simplify terms.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{4 \sqrt{15}}{3 \sqrt{14}}$ by $\frac{\sqrt{14}}{\sqrt{14}}$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 \sqrt{14} \sqrt{14}}$

Step 2.1.2

Move $\sqrt{14}$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 (\sqrt{14} \sqrt{14})}$

Step 2.1.3

Raise $\sqrt{14}$ to the power of $1$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 ({\sqrt{14}}^{1} \sqrt{14})}$

Step 2.1.4

Raise $\sqrt{14}$ to the power of $1$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 ({\sqrt{14}}^{1} {\sqrt{14}}^{1})}$

Step 2.1.5

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

$\frac{4 \sqrt{15} \sqrt{14}}{3 {\sqrt{14}}^{1 + 1}}$

Step 2.1.6

Add $1$ and $1$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 {\sqrt{14}}^{2}}$

Step 2.1.7

Rewrite ${\sqrt{14}}^{2}$ as $14$ .

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Step 2.1.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14}$ as $14^{\frac{1}{2}}$ .

$\frac{4 \sqrt{15} \sqrt{14}}{3 {(14^{\frac{1}{2}})}^{2}}$

Step 2.1.7.2

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

$\frac{4 \sqrt{15} \sqrt{14}}{3 \cdot 14^{\frac{1}{2} \cdot 2}}$

Step 2.1.7.3

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

$\frac{4 \sqrt{15} \sqrt{14}}{3 \cdot 14^{\frac{2}{2}}}$

Step 2.1.7.4

Cancel the common factor of $2$ .

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Step 2.1.7.4.1

Cancel the common factor.

$\frac{4 \sqrt{15} \sqrt{14}}{3 \cdot 14^{\frac{2}{2}}}$

Step 2.1.7.4.2

Rewrite the expression.

$\frac{4 \sqrt{15} \sqrt{14}}{3 \cdot 14^{1}}$

Step 2.1.7.5

Evaluate the exponent.

$\frac{4 \sqrt{15} \sqrt{14}}{3 \cdot 14}$

Step 2.2

Cancel the common factor of $4$ and $14$ .

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Step 2.2.1

Factor $2$ out of $4 \sqrt{15} \sqrt{14}$ .

$\frac{2 (2 \sqrt{15} \sqrt{14})}{3 \cdot 14}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $3 \cdot 14$ .

$\frac{2 (2 \sqrt{15} \sqrt{14})}{2 (3 \cdot 7)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 (2 \sqrt{15} \sqrt{14})}{2 (3 \cdot 7)}$

Step 2.2.2.3

Rewrite the expression.

$\frac{2 \sqrt{15} \sqrt{14}}{3 \cdot 7}$

Step 3

Simplify the numerator.

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Step 3.1

Combine using the product rule for radicals.

$\frac{2 \sqrt{14 \cdot 15}}{3 \cdot 7}$

Step 3.2

Multiply $14$ by $15$ .

$\frac{2 \sqrt{210}}{3 \cdot 7}$

Step 4

Multiply $3$ by $7$ .

$\frac{2 \sqrt{210}}{21}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{210}}{21}$

Decimal Form:

$1.38013111 \dots$