Basic Math Examples

\frac{\sqrt{7}}{7} + \frac{1}{\sqrt{7}}

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

Step 1

Simplify each term.

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Step 1.1

Multiply

\frac{1}{\sqrt{7}}

$\frac{1}{\sqrt{7}}$ by

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

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

\frac{\sqrt{7}}{7} + \frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}

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

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply

\frac{1}{\sqrt{7}}

$\frac{1}{\sqrt{7}}$ by

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

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

\frac{\sqrt{7}}{7} + \frac{\sqrt{7}}{\sqrt{7} \sqrt{7}}

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

Step 1.2.2

Raise

\sqrt{7}

$\sqrt{7}$ to the power of

1

$1$ .

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

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

Step 1.2.3

Raise

\sqrt{7}

$\sqrt{7}$ to the power of

1

$1$ .

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

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

Step 1.2.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 1.2.5

Add

1

$1$ and

1

$1$ .

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

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

Step 1.2.6

Rewrite

{\sqrt{7}}^{2}

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

7

$7$ .

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Step 1.2.6.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{7}

$\sqrt{7}$ as

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

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

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

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

Step 1.2.6.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 1.2.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 1.2.6.4

Cancel the common factor of

2

$2$ .

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Step 1.2.6.4.1

Cancel the common factor.

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

Step 1.2.6.4.2

Rewrite the expression.

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

Step 1.2.6.5

Evaluate the exponent.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add

$\sqrt{7}$ and

$\sqrt{7}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.75592894 \dots$