Evaluate square root of -3* square root of -21

$\sqrt{- 3} \cdot \sqrt{- 21}$

Step 1

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

$\sqrt{- 1 (3)} \cdot \sqrt{- 21}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{3} \cdot \sqrt{- 21}$

Step 3

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

$i \cdot \sqrt{3} \cdot \sqrt{- 21}$

Step 4

Rewrite $- 21$ as $- 1 (21)$ .

$i \cdot \sqrt{3} \cdot \sqrt{- 1 (21)}$

Step 5

Rewrite $\sqrt{- 1 (21)}$ as $\sqrt{- 1} \cdot \sqrt{21}$ .

$i \cdot \sqrt{3} \cdot (\sqrt{- 1} \cdot \sqrt{21})$

Step 6

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

$i \cdot \sqrt{3} \cdot (i \cdot \sqrt{21})$

Step 7

Multiply $i \sqrt{3} (i \sqrt{21})$ .

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

$i^{1} i \sqrt{3} \sqrt{21}$

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

$i^{1} i^{1} \sqrt{3} \sqrt{21}$

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

$i^{1 + 1} \sqrt{3} \sqrt{21}$

Add $1$ and $1$ .

$i^{2} \sqrt{3} \sqrt{21}$

Combine using the product rule for radicals.

$i^{2} \sqrt{21 \cdot 3}$

Multiply $21$ by $3$ .

$i^{2} \sqrt{63}$

Step 8

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

$- 1 \sqrt{63}$

Step 9

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$- 1 \sqrt{9 (7)}$

Rewrite $9$ as $3^{2}$ .

$- 1 \sqrt{3^{2} \cdot 7}$

Step 10

Pull terms out from under the radical.

$- 1 (3 \sqrt{7})$

Step 11

Multiply $3$ by $- 1$ .

$- 3 \sqrt{7}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{7}$

Decimal Form:

$- 7.93725393 \dots$

Evaluate square root of -3* square root of -21

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