Algebra Examples

$\frac{\sqrt{8}}{2 \sqrt{14}}$

Step 1

Combine $\sqrt{8}$ and $\sqrt{14}$ into a single radical.

$\frac{\sqrt{\frac{8}{14}}}{2}$

Step 2

Cancel the common factor of $8$ and $14$ .

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Step 2.1

Factor $2$ out of $8$ .

$\frac{\sqrt{\frac{2 (4)}{14}}}{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $14$ .

$\frac{\sqrt{\frac{2 \cdot 4}{2 \cdot 7}}}{2}$

Step 2.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{2 \cdot 4}{2 \cdot 7}}}{2}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{\frac{4}{7}}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt{\frac{4}{7}}$ as $\frac{\sqrt{4}}{\sqrt{7}}$ .

$\frac{\frac{\sqrt{4}}{\sqrt{7}}}{2}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Rewrite $4$ as $2^{2}$ .

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

Step 3.2.2

Pull terms out from under the radical.

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

Step 3.2.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 3.3

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

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

Step 3.4

Combine and simplify the denominator.

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Step 3.4.1

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

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

Step 3.4.2

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

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

Step 3.4.3

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

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

Step 3.4.4

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

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

Step 3.4.5

Add $1$ and $1$ .

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

Step 3.4.6

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

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Step 3.4.6.1

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

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

Step 3.4.6.2

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

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

Step 3.4.6.3

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

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

Step 3.4.6.4

Cancel the common factor of $2$ .

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Step 3.4.6.4.1

Cancel the common factor.

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

Step 3.4.6.4.2

Rewrite the expression.

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

Step 3.4.6.5

Evaluate the exponent.

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $2 \sqrt{7}$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.37796447 \dots$