Basic Math Examples

\sqrt{{(\frac{h}{2})}^{2} + {(\frac{h}{2})}^{2}}

$\sqrt{{(\frac{h}{2})}^{2} + {(\frac{h}{2})}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to

\frac{h}{2}

$\frac{h}{2}$ .

\sqrt{\frac{h^{2}}{2^{2}} + {(\frac{h}{2})}^{2}}

$\sqrt{\frac{h^{2}}{2^{2}} + {(\frac{h}{2})}^{2}}$

Step 1.2

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{\frac{h^{2}}{4} + {(\frac{h}{2})}^{2}}

$\sqrt{\frac{h^{2}}{4} + {(\frac{h}{2})}^{2}}$

Step 1.3

Apply the product rule to

\frac{h}{2}

$\frac{h}{2}$ .

\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{2^{2}}}

$\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{2^{2}}}$

Step 1.4

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{4}}

$\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{4}}$

\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{4}}

$\sqrt{\frac{h^{2}}{4} + \frac{h^{2}}{4}}$

Step 2

Add

\frac{h^{2}}{4}

$\frac{h^{2}}{4}$ and

\frac{h^{2}}{4}

$\frac{h^{2}}{4}$ .

\sqrt{2 \frac{h^{2}}{4}}

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

Step 3

Combine

2

$2$ and

\frac{h^{2}}{4}

$\frac{h^{2}}{4}$ .

\sqrt{\frac{2 h^{2}}{4}}

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

Step 4

Reduce the expression

\frac{2 h^{2}}{4}

$\frac{2 h^{2}}{4}$ by cancelling the common factors.

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Step 4.1

Factor

2

$2$ out of

2 h^{2}

$2 h^{2}$ .

\sqrt{\frac{2 (h^{2})}{4}}

$\sqrt{\frac{2 (h^{2})}{4}}$

Step 4.2

Factor

2

$2$ out of

4

$4$ .

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

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

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

Step 5

Rewrite

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

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

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

Step 6

Pull terms out from under the radical, assuming positive real numbers.

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

Step 7

Multiply

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

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

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

Step 8

Combine and simplify the denominator.

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Step 8.1

Multiply

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

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

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

Step 8.2

Raise

$\sqrt{2}$ to the power of

$1$ .

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

Step 8.3

Raise

$\sqrt{2}$ to the power of

$1$ .

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

Step 8.4

Use the power rule

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

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

Step 8.5

Add

$1$ and

$1$ .

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

Step 8.6

Rewrite

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

$2$ .

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Step 8.6.1

Use

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

$\sqrt{2}$ as

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

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

Step 8.6.2

Apply the power rule and multiply exponents,

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

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

Step 8.6.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 8.6.4

Cancel the common factor of

$2$ .

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Step 8.6.4.1

Cancel the common factor.

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

Step 8.6.4.2

Rewrite the expression.

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

Step 8.6.5

Evaluate the exponent.

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