Basic Math Examples

$(\sqrt{- 20}) (\sqrt{- 13})$

Step 1

Rewrite $- 20$ as $- 1 (20)$ .

$\sqrt{- 1 (20)} \sqrt{- 13}$

Step 2

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\sqrt{- 1} \cdot \sqrt{20} \sqrt{- 13}$

Step 3

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

$i \cdot \sqrt{20} \sqrt{- 13}$

Step 4

Rewrite $- 13$ as $- 1 (13)$ .

$i \cdot \sqrt{20} \sqrt{- 1 (13)}$

Step 5

Rewrite $\sqrt{- 1 (13)}$ as $\sqrt{- 1} \cdot \sqrt{13}$ .

$i \cdot \sqrt{20} (\sqrt{- 1} \cdot \sqrt{13})$

Step 6

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

$i \cdot \sqrt{20} (i \cdot \sqrt{13})$

Step 7

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 7.1

Factor $4$ out of $20$ .

$i \cdot \sqrt{4 (5)} (i \cdot \sqrt{13})$

Step 7.2

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

$i \cdot \sqrt{2^{2} \cdot 5} (i \cdot \sqrt{13})$

Step 8

Pull terms out from under the radical.

$i \cdot (2 \sqrt{5}) (i \cdot \sqrt{13})$

Step 9

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

$2 \cdot i \sqrt{5} (i \cdot \sqrt{13})$

Step 10

Multiply $2 i \sqrt{5} (i \sqrt{13})$ .

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Step 10.1

Raise $i$ to the power of $1$ .

$2 (i^{1} i) \sqrt{5} \sqrt{13}$

Step 10.2

Raise $i$ to the power of $1$ .

$2 (i^{1} i^{1}) \sqrt{5} \sqrt{13}$

Step 10.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 i^{1 + 1} \sqrt{5} \sqrt{13}$

Step 10.4

Add $1$ and $1$ .

$2 i^{2} \sqrt{5} \sqrt{13}$

Step 10.5

Combine using the product rule for radicals.

$2 i^{2} \sqrt{13 \cdot 5}$

Step 10.6

Multiply $13$ by $5$ .

$2 i^{2} \sqrt{65}$

Step 11

Rewrite $i^{2}$ as $- 1$ .

$2 \cdot - 1 \sqrt{65}$

Step 12

Multiply $2$ by $- 1$ .

$- 2 \sqrt{65}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{65}$

Decimal Form:

$- 16.12451549 \dots$