Basic Math Examples

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

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{h}{2}$ .

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

Step 1.2

Raise $2$ to the power of $2$ .

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

Step 1.3

Apply the product rule to $\frac{h}{2}$ .

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

Step 1.4

Raise $2$ to the power of $2$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

Factor $2$ out of $2 h^{2}$ .

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

Step 4.2

Factor $2$ out of $4$ .

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

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.

Tap for more steps...

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 $2$ .

Tap for more steps...

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 $2$ .

Tap for more steps...

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.

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