Basic Math Examples

$\sqrt{- 13} \cdot \sqrt{- 14}$

Step 1

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

$\sqrt{- 1 (13)} \cdot \sqrt{- 14}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{13} \cdot \sqrt{- 14}$

Step 3

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

$i \cdot \sqrt{13} \cdot \sqrt{- 14}$

Step 4

Rewrite $- 14$ as $- 1 (14)$ .

$i \cdot \sqrt{13} \cdot \sqrt{- 1 (14)}$

Step 5

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$i \cdot \sqrt{13} \cdot (\sqrt{- 1} \cdot \sqrt{14})$

Step 6

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

$i \cdot \sqrt{13} \cdot (i \cdot \sqrt{14})$

Step 7

Multiply $i \sqrt{13} (i \sqrt{14})$ .

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Step 7.1

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

$i^{1} i \sqrt{13} \sqrt{14}$

Step 7.2

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

$i^{1} i^{1} \sqrt{13} \sqrt{14}$

Step 7.3

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

$i^{1 + 1} \sqrt{13} \sqrt{14}$

Step 7.4

Add $1$ and $1$ .

$i^{2} \sqrt{13} \sqrt{14}$

Step 7.5

Combine using the product rule for radicals.

$i^{2} \sqrt{14 \cdot 13}$

Step 7.6

Multiply $14$ by $13$ .

$i^{2} \sqrt{182}$

Step 8

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

$- 1 \sqrt{182}$

Step 9

Rewrite $- 1 \sqrt{182}$ as $- \sqrt{182}$ .

$- \sqrt{182}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{182}$

Decimal Form:

$- 13.49073756 \dots$