Precalculus Examples

$\frac{\sqrt{- 7} \sqrt{- 49}}{\sqrt{28}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{\sqrt{- 1 (7)} \sqrt{- 49}}{\sqrt{28}}$

Step 1.2

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{7} \sqrt{- 49}}{\sqrt{28}}$

Step 1.3

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{7} \sqrt{- 49}}{\sqrt{28}}$

Step 1.4

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{i \cdot \sqrt{7} \sqrt{- 1 (49)}}{\sqrt{28}}$

Step 1.5

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$\frac{i \cdot \sqrt{7} (\sqrt{- 1} \cdot \sqrt{49})}{\sqrt{28}}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{7} (i \cdot \sqrt{49})}{\sqrt{28}}$

Step 2

Combine $\sqrt{7}$ and $\sqrt{28}$ into a single radical.

$i \cdot \sqrt{\frac{7}{28}} i \cdot \sqrt{49}$

Step 3

Cancel the common factor of $7$ and $28$ .

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Step 3.1

Factor $7$ out of $7$ .

$i \cdot \sqrt{\frac{7 (1)}{28}} i \cdot \sqrt{49}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $28$ .

$i \cdot \sqrt{\frac{7 \cdot 1}{7 \cdot 4}} i \cdot \sqrt{49}$

Step 3.2.2

Cancel the common factor.

$i \cdot \sqrt{\frac{7 \cdot 1}{7 \cdot 4}} i \cdot \sqrt{49}$

Step 3.2.3

Rewrite the expression.

$i \cdot \sqrt{\frac{1}{4}} i \cdot \sqrt{49}$

Step 4

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$i \cdot \frac{\sqrt{1}}{\sqrt{4}} i \cdot \sqrt{49}$

Step 5

Any root of $1$ is $1$ .

$i \cdot \frac{1}{\sqrt{4}} i \cdot \sqrt{49}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $4$ as $2^{2}$ .

$i \cdot \frac{1}{\sqrt{2^{2}}} i \cdot \sqrt{49}$

Step 6.2

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

$i \cdot \frac{1}{2} i \cdot \sqrt{49}$

Step 7

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

$\frac{i}{2} i \cdot \sqrt{49}$

Step 8

Multiply $\frac{i}{2} i$ .

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Step 8.1

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

$\frac{i i}{2} \cdot \sqrt{49}$

Step 8.2

Raise $i$ to the power of $1$ .

$\frac{i^{1} i}{2} \cdot \sqrt{49}$

Step 8.3

Raise $i$ to the power of $1$ .

$\frac{i^{1} i^{1}}{2} \cdot \sqrt{49}$

Step 8.4

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

$\frac{i^{1 + 1}}{2} \cdot \sqrt{49}$

Step 8.5

Add $1$ and $1$ .

$\frac{i^{2}}{2} \cdot \sqrt{49}$

Step 9

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 1}{2} \cdot \sqrt{49}$

Step 10

Move the negative in front of the fraction.

$- \frac{1}{2} \cdot \sqrt{49}$

Step 11

Rewrite $49$ as $7^{2}$ .

$- \frac{1}{2} \cdot \sqrt{7^{2}}$

Step 12

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

$- \frac{1}{2} \cdot 7$

Step 13

Multiply $- \frac{1}{2} \cdot 7$ .

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Step 13.1

Multiply $7$ by $- 1$ .

$- 7 (\frac{1}{2})$

Step 13.2

Combine $- 7$ and $\frac{1}{2}$ .

$\frac{- 7}{2}$

Step 14

Move the negative in front of the fraction.

$- \frac{7}{2}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{2}$

Decimal Form:

$- 3.5$

Mixed Number Form:

$- 3 \frac{1}{2}$