Algebra Examples

$\frac{4}{5} - \frac{2}{7} \sqrt{- 98}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 98$ as $- 1 (98)$ .

$\frac{4}{5} - \frac{2}{7} \cdot \sqrt{- 1 (98)}$

Step 1.2

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$\frac{4}{5} - \frac{2}{7} \cdot (\sqrt{- 1} \cdot \sqrt{98})$

Step 1.3

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

$\frac{4}{5} - \frac{2}{7} \cdot (i \cdot \sqrt{98})$

Step 1.4

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.4.1

Factor $49$ out of $98$ .

$\frac{4}{5} - \frac{2}{7} \cdot (i \cdot \sqrt{49 (2)})$

Step 1.4.2

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

$\frac{4}{5} - \frac{2}{7} \cdot (i \cdot \sqrt{7^{2} \cdot 2})$

Step 1.5

Pull terms out from under the radical.

$\frac{4}{5} - \frac{2}{7} \cdot (i \cdot (7 \sqrt{2}))$

Step 1.6

Cancel the common factor of $7$ .

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Step 1.6.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{4}{5} + \frac{- 2}{7} \cdot (i \cdot (7 \sqrt{2}))$

Step 1.6.2

Factor $7$ out of $i \cdot (7 \sqrt{2})$ .

$\frac{4}{5} + \frac{- 2}{7} \cdot (7 (i \cdot (\sqrt{2})))$

Step 1.6.3

Cancel the common factor.

$\frac{4}{5} + \frac{- 2}{7} \cdot (7 (i \cdot (\sqrt{2})))$

Step 1.6.4

Rewrite the expression.

$\frac{4}{5} - 2 \cdot (i \cdot (\sqrt{2}))$

$\frac{4}{5} - 2 i \sqrt{2}$

Step 2

To write $- 2 i \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{5} - 2 i \sqrt{2} \cdot \frac{5}{5}$

Step 3

Combine $- 2 i \sqrt{2}$ and $\frac{5}{5}$ .

$\frac{4}{5} + \frac{- 2 i \sqrt{2} \cdot 5}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 - 10 i \sqrt{2}}{5}$