Basic Math Examples

\frac{\sqrt{- 54}}{\sqrt{- 9}}

$\frac{\sqrt{- 54}}{\sqrt{- 9}}$

Step 1

Pull out imaginary unit

i

$i$ .

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Step 1.1

Rewrite

- 54

$- 54$ as

- 1 (54)

$- 1 (54)$ .

\frac{\sqrt{- 1 (54)}}{\sqrt{- 9}}

$\frac{\sqrt{- 1 (54)}}{\sqrt{- 9}}$

Step 1.2

Rewrite

\sqrt{- 1 (54)}

$\sqrt{- 1 (54)}$ as

\sqrt{- 1} \cdot \sqrt{54}

$\sqrt{- 1} \cdot \sqrt{54}$ .

\frac{\sqrt{- 1} \cdot \sqrt{54}}{\sqrt{- 9}}

$\frac{\sqrt{- 1} \cdot \sqrt{54}}{\sqrt{- 9}}$

Step 1.3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

\frac{i \cdot \sqrt{54}}{\sqrt{- 9}}

$\frac{i \cdot \sqrt{54}}{\sqrt{- 9}}$

Step 1.4

Rewrite

- 9

$- 9$ as

- 1 (9)

$- 1 (9)$ .

\frac{i \cdot \sqrt{54}}{\sqrt{- 1 (9)}}

$\frac{i \cdot \sqrt{54}}{\sqrt{- 1 (9)}}$

Step 1.5

Rewrite

\sqrt{- 1 (9)}

$\sqrt{- 1 (9)}$ as

\sqrt{- 1} \cdot \sqrt{9}

$\sqrt{- 1} \cdot \sqrt{9}$ .

\frac{i \cdot \sqrt{54}}{\sqrt{- 1} \cdot \sqrt{9}}

$\frac{i \cdot \sqrt{54}}{\sqrt{- 1} \cdot \sqrt{9}}$

Step 1.6

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{9}}

$\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{9}}$

$\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{9}}$

Step 2

Cancel the common factor of

$i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{54}}{i \cdot \sqrt{9}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{54}}{\sqrt{9}}$

$\frac{\sqrt{54}}{\sqrt{9}}$

Step 3

Combine

$\sqrt{54}$ and

$\sqrt{9}$ into a single radical.

$\sqrt{\frac{54}{9}}$

Step 4

Divide

$54$ by

$9$ .

$\sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{6}$

Decimal Form:

$2.44948974 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$