Basic Math Examples

$\frac{\sqrt{10}}{10} + \frac{1}{\sqrt{10}}$

Step 1

Simplify each term.

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Step 1.1

Multiply

$\frac{1}{\sqrt{10}}$ by

$\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{10} + \frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply

$\frac{1}{\sqrt{10}}$ by

$\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{\sqrt{10} \sqrt{10}}$

Step 1.2.2

Raise

$\sqrt{10}$ to the power of

$1$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Step 1.2.3

Raise

$\sqrt{10}$ to the power of

$1$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Step 1.2.4

Use the power rule

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

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Step 1.2.5

Add

$1$ and

$1$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{{\sqrt{10}}^{2}}$

Step 1.2.6

Rewrite

${\sqrt{10}}^{2}$ as

$10$ .

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Step 1.2.6.1

Use

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

$\sqrt{10}$ as

$10^{\frac{1}{2}}$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Step 1.2.6.2

Apply the power rule and multiply exponents,

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

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Step 1.2.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Step 1.2.6.4

Cancel the common factor of

$2$ .

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Step 1.2.6.4.1

Cancel the common factor.

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Step 1.2.6.4.2

Rewrite the expression.

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{10^{1}}$

Step 1.2.6.5

Evaluate the exponent.

$\frac{\sqrt{10}}{10} + \frac{\sqrt{10}}{10}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\sqrt{10} + \sqrt{10}}{10}$

Step 2.2

Add

$\sqrt{10}$ and

$\sqrt{10}$ .

$\frac{2 \sqrt{10}}{10}$

Step 2.3

Cancel the common factor of

$2$ and

$10$ .

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Step 2.3.1

Factor

$2$ out of

$2 \sqrt{10}$ .

$\frac{2 (\sqrt{10})}{10}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor

$2$ out of

$10$ .

$\frac{2 \sqrt{10}}{2 \cdot 5}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 \sqrt{10}}{2 \cdot 5}$

Step 2.3.2.3

Rewrite the expression.

$\frac{\sqrt{10}}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{5}$

Decimal Form:

$0.63245553 \dots$