Basic Math Examples

$\sqrt{\frac{1}{33}}$

Step 1

Rewrite $\sqrt{\frac{1}{33}}$ as $\frac{\sqrt{1}}{\sqrt{33}}$ .

$\frac{\sqrt{1}}{\sqrt{33}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{33}}$

Step 3

Multiply $\frac{1}{\sqrt{33}}$ by $\frac{\sqrt{33}}{\sqrt{33}}$ .

$\frac{1}{\sqrt{33}} \cdot \frac{\sqrt{33}}{\sqrt{33}}$

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{1}{\sqrt{33}}$ by $\frac{\sqrt{33}}{\sqrt{33}}$ .

$\frac{\sqrt{33}}{\sqrt{33} \sqrt{33}}$

Step 4.2

Raise $\sqrt{33}$ to the power of $1$ .

$\frac{\sqrt{33}}{{\sqrt{33}}^{1} \sqrt{33}}$

Step 4.3

Raise $\sqrt{33}$ to the power of $1$ .

$\frac{\sqrt{33}}{{\sqrt{33}}^{1} {\sqrt{33}}^{1}}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{33}}{{\sqrt{33}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{33}}{{\sqrt{33}}^{2}}$

Step 4.6

Rewrite ${\sqrt{33}}^{2}$ as $33$ .

Tap for more steps...

Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{33}$ as $33^{\frac{1}{2}}$ .

$\frac{\sqrt{33}}{{(33^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{33}}{33^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{33}}{33^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{33}}{33^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{33}}{33^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{33}}{33}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{33}}{33}$

Decimal Form:

$0.17407765 \dots$