Algebra Examples

$\frac{3 \sqrt{7}}{14}$

Step 1

Multiply to rationalize the numerator.

$\frac{3 (\sqrt{7} \sqrt{7})}{14 \sqrt{7}}$

Step 2

Simplify.

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Step 2.1

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

$\frac{3 ({\sqrt{7}}^{1} \sqrt{7})}{14 \sqrt{7}}$

Step 2.2

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

$\frac{3 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}{14 \sqrt{7}}$

Step 2.3

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

$\frac{3 {\sqrt{7}}^{1 + 1}}{14 \sqrt{7}}$

Step 2.4

Add $1$ and $1$ .

$\frac{3 {\sqrt{7}}^{2}}{14 \sqrt{7}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{3 {(7^{\frac{1}{2}})}^{2}}{14 \sqrt{7}}$

Step 2.5.2

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

$\frac{3 \cdot 7^{\frac{1}{2} \cdot 2}}{14 \sqrt{7}}$

Step 2.5.3

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

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

Step 2.5.4

Cancel the common factor of $2$ .

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Step 2.5.4.1

Cancel the common factor.

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

Step 2.5.4.2

Rewrite the expression.

$\frac{3 \cdot 7^{1}}{14 \sqrt{7}}$

Step 2.5.5

Evaluate the exponent.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.56694670 \dots$