Algebra Examples

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

Step 1

Rewrite $- 40$ as $- 1 (40)$ .

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

Step 2

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

Factor $4$ out of $40$ .

$i \cdot \sqrt{4 (10)} (- \sqrt{5})$

Step 4.2

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

$i \cdot \sqrt{2^{2} \cdot 10} (- \sqrt{5})$

$i \cdot \sqrt{2^{2} \cdot 10} (- \sqrt{5})$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{10}) (- \sqrt{5})$

Step 6

Move $2$ to the left of $i$ .

$2 \cdot i \sqrt{10} (- \sqrt{5})$

Step 7

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

Tap for more steps...

Step 7.1

Multiply $- 1$ by $2$ .

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

Step 7.2

Combine using the product rule for radicals.

$- 2 i \sqrt{5 \cdot 10}$

Step 7.3

Multiply $5$ by $10$ .

$- 2 i \sqrt{50}$

$- 2 i \sqrt{50}$

Step 8

Rewrite $50$ as $5^{2} \cdot 2$ .

Tap for more steps...

Step 8.1

Factor $25$ out of $50$ .

$- 2 i \sqrt{25 (2)}$

Step 8.2

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

$- 2 i \sqrt{5^{2} \cdot 2}$

$- 2 i \sqrt{5^{2} \cdot 2}$

Step 9

Pull terms out from under the radical.

$- 2 i (5 \sqrt{2})$

Step 10

Multiply $5$ by $- 2$ .

$- 10 i \sqrt{2}$

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