Basic Math Examples

\frac{1}{2 \sqrt{2}}

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

Step 1

Multiply

\frac{1}{2 \sqrt{2}}

$\frac{1}{2 \sqrt{2}}$ by

\frac{\sqrt{2}}{\sqrt{2}}

$\frac{\sqrt{2}}{\sqrt{2}}$ .

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

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

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

\frac{1}{2 \sqrt{2}}

$\frac{1}{2 \sqrt{2}}$ by

\frac{\sqrt{2}}{\sqrt{2}}

$\frac{\sqrt{2}}{\sqrt{2}}$ .

\frac{\sqrt{2}}{2 \sqrt{2} \sqrt{2}}

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

Step 2.2

Move

\sqrt{2}

$\sqrt{2}$ .

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

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

Step 2.3

Raise

\sqrt{2}

$\sqrt{2}$ to the power of

1

$1$ .

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

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

Step 2.4

Raise

\sqrt{2}

$\sqrt{2}$ to the power of

1

$1$ .

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

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

Step 2.5

Use the power rule

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

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

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

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

Step 2.6

Add

1

$1$ and

1

$1$ .

\frac{\sqrt{2}}{2 {\sqrt{2}}^{2}}

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

Step 2.7

Rewrite

{\sqrt{2}}^{2}

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

2

$2$ .

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Step 2.7.1

Use

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

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

\sqrt{2}

$\sqrt{2}$ as

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

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

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

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

Step 2.7.2

Apply the power rule and multiply exponents,

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

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

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

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

Step 2.7.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{\sqrt{2}}{2 \cdot 2^{\frac{2}{2}}}

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

Step 2.7.4

Cancel the common factor of

2

$2$ .

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Step 2.7.4.1

Cancel the common factor.

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

Step 2.7.4.2

Rewrite the expression.

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

Step 2.7.5

Evaluate the exponent.

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

Step 3

Multiply

$2$ by

$2$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.35355339 \dots$