Evaluate square root of -14* square root of -17

$\sqrt{- 14} \cdot \sqrt{- 17}$

Step 1

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

$\sqrt{- 1 (14)} \cdot \sqrt{- 17}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{14} \cdot \sqrt{- 17}$

Step 3

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

$i \cdot \sqrt{14} \cdot \sqrt{- 17}$

Step 4

Rewrite $- 17$ as $- 1 (17)$ .

$i \cdot \sqrt{14} \cdot \sqrt{- 1 (17)}$

Step 5

Rewrite $\sqrt{- 1 (17)}$ as $\sqrt{- 1} \cdot \sqrt{17}$ .

$i \cdot \sqrt{14} \cdot (\sqrt{- 1} \cdot \sqrt{17})$

Step 6

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

$i \cdot \sqrt{14} \cdot (i \cdot \sqrt{17})$

Step 7

Multiply $i \sqrt{14} (i \sqrt{17})$ .

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

$i^{1} i \sqrt{14} \sqrt{17}$

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

$i^{1} i^{1} \sqrt{14} \sqrt{17}$

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

$i^{1 + 1} \sqrt{14} \sqrt{17}$

Add $1$ and $1$ .

$i^{2} \sqrt{14} \sqrt{17}$

Combine using the product rule for radicals.

$i^{2} \sqrt{17 \cdot 14}$

Multiply $17$ by $14$ .

$i^{2} \sqrt{238}$

Step 8

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

$- 1 \sqrt{238}$

Step 9

Rewrite $- 1 \sqrt{238}$ as $- \sqrt{238}$ .

$- \sqrt{238}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{238}$

Decimal Form:

$- 15.42724862 \dots$