Algebra Examples

$(5 \sqrt{- 70}) (\sqrt{40})$

Step 1

Rewrite $- 70$ as $- 1 (70)$ .

$5 \sqrt{- 1 (70)} \sqrt{40}$

Step 2

Rewrite $\sqrt{- 1 (70)}$ as $\sqrt{- 1} \cdot \sqrt{70}$ .

$5 (\sqrt{- 1} \cdot \sqrt{70}) \sqrt{40}$

Step 3

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

$5 (i \cdot \sqrt{70}) \sqrt{40}$

Step 4

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 4.1

Factor $4$ out of $40$ .

$5 i \sqrt{70} \sqrt{4 (10)}$

Step 4.2

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

$5 i \sqrt{70} \sqrt{2^{2} \cdot 10}$

$5 i \sqrt{70} \sqrt{2^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$5 i \sqrt{70} (2 \sqrt{10})$

Step 6

Multiply $5 i \sqrt{70} (2 \sqrt{10})$ .

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Step 6.1

Multiply $2$ by $5$ .

$10 i \sqrt{70} \sqrt{10}$

Step 6.2

Combine using the product rule for radicals.

$10 i \sqrt{10 \cdot 70}$

Step 6.3

Multiply $10$ by $70$ .

$10 i \sqrt{700}$

$10 i \sqrt{700}$

Step 7

Rewrite $700$ as $10^{2} \cdot 7$ .

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Step 7.1

Factor $100$ out of $700$ .

$10 i \sqrt{100 (7)}$

Step 7.2

Rewrite $100$ as $10^{2}$ .

$10 i \sqrt{10^{2} \cdot 7}$

$10 i \sqrt{10^{2} \cdot 7}$

Step 8

Pull terms out from under the radical.

$10 i (10 \sqrt{7})$

Step 9

Multiply $10$ by $10$ .

$100 i \sqrt{7}$

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