Algebra Examples

$(\sqrt{- 15}) (- 7 \sqrt{5})$

Step 1

Rewrite $- 15$ as $- 1 (15)$ .

$\sqrt{- 1 (15)} (- 7 \sqrt{5})$

Step 2

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$\sqrt{- 1} \cdot \sqrt{15} (- 7 \sqrt{5})$

Step 3

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

$i \cdot \sqrt{15} (- 7 \sqrt{5})$

Step 4

Multiply $i \sqrt{15} (- 7 \sqrt{5})$ .

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Step 4.1

Combine using the product rule for radicals.

$i (- 7 \sqrt{15 \cdot 5})$

Step 4.2

Multiply $15$ by $5$ .

$i (- 7 \sqrt{75})$

$i (- 7 \sqrt{75})$

Step 5

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 5.1

Factor $25$ out of $75$ .

$i (- 7 \sqrt{25 (3)})$

Step 5.2

Rewrite $25$ as $5^{2}$ .

$i (- 7 \sqrt{5^{2} \cdot 3})$

$i (- 7 \sqrt{5^{2} \cdot 3})$

Step 6

Pull terms out from under the radical.

$i (- 7 (5 \sqrt{3}))$

Step 7

Simplify the expression.

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Step 7.1

Multiply $5$ by $- 7$ .

$i (- 35 \sqrt{3})$

Step 7.2

Reorder factors in $i (- 35 \sqrt{3})$ .

$- 35 i \sqrt{3}$

$- 35 i \sqrt{3}$

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