Simplify square root of -5* square root of -3

$\sqrt{- 5} \cdot \sqrt{- 3}$

Step 1

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt{- 1 (5)} \cdot \sqrt{- 3}$

Step 2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{- 3}$

Step 3

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

$i \cdot \sqrt{5} \cdot \sqrt{- 3}$

Step 4

Rewrite $- 3$ as $- 1 (3)$ .

$i \cdot \sqrt{5} \cdot \sqrt{- 1 (3)}$

Step 5

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$i \cdot \sqrt{5} \cdot (\sqrt{- 1} \cdot \sqrt{3})$

Step 6

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

$i \cdot \sqrt{5} \cdot (i \cdot \sqrt{3})$

Step 7

Multiply $i \sqrt{5} (i \sqrt{3})$ .

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

$i^{1} i \sqrt{5} \sqrt{3}$

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

$i^{1} i^{1} \sqrt{5} \sqrt{3}$

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

$i^{1 + 1} \sqrt{5} \sqrt{3}$

Add $1$ and $1$ .

$i^{2} \sqrt{5} \sqrt{3}$

Combine using the product rule for radicals.

$i^{2} \sqrt{3 \cdot 5}$

Multiply $3$ by $5$ .

$i^{2} \sqrt{15}$

Step 8

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

$- 1 \sqrt{15}$

Step 9

Rewrite $- 1 \sqrt{15}$ as $- \sqrt{15}$ .

$- \sqrt{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{15}$

Decimal Form:

$- 3.87298334 \dots$