Algebra Examples

$(10 \sqrt{40}) (\sqrt{- 9})$

Step 1

Rewrite $- 9$ as $- 1 (9)$ .

$10 \sqrt{40} \sqrt{- 1 (9)}$

Step 2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$10 \sqrt{40} (\sqrt{- 1} \cdot \sqrt{9})$

Step 3

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

$10 \sqrt{40} (i \cdot \sqrt{9})$

Step 4

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

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Step 4.1

Factor $4$ out of $40$ .

$10 \sqrt{4 (10)} (i \cdot \sqrt{9})$

Step 4.2

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

$10 \sqrt{2^{2} \cdot 10} (i \cdot \sqrt{9})$

Step 5

Pull terms out from under the radical.

$10 (2 \sqrt{10}) (i \cdot \sqrt{9})$

Step 6

Write the expression using exponents.

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Step 6.1

Multiply $2$ by $10$ .

$20 \sqrt{10} (i \cdot \sqrt{9})$

Step 6.2

Rewrite $9$ as $3^{2}$ .

$20 \sqrt{10} (i \cdot \sqrt{3^{2}})$

Step 7

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

$20 \sqrt{10} (i \cdot 3)$

Step 8

Move $3$ to the left of $i$ .

$20 \sqrt{10} (3 \cdot i)$

Step 9

Multiply $3$ by $20$ .

$60 \sqrt{10} i$