Algebra Examples

$(- 9 \sqrt{- 42}) (5 \sqrt{- 6})$

Step 1

Rewrite $- 42$ as $- 1 (42)$ .

$- 9 \sqrt{- 1 (42)} (5 \sqrt{- 6})$

Step 2

Rewrite $\sqrt{- 1 (42)}$ as $\sqrt{- 1} \cdot \sqrt{42}$ .

$- 9 (\sqrt{- 1} \cdot \sqrt{42}) (5 \sqrt{- 6})$

Step 3

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

$- 9 (i \cdot \sqrt{42}) (5 \sqrt{- 6})$

Step 4

Rewrite $- 6$ as $- 1 (6)$ .

$- 9 (i \cdot \sqrt{42}) (5 \sqrt{- 1 (6)})$

Step 5

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$- 9 (i \cdot \sqrt{42}) (5 (\sqrt{- 1} \cdot \sqrt{6}))$

Step 6

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

$- 9 (i \cdot \sqrt{42}) (5 (i \cdot \sqrt{6}))$

Step 7

Multiply $- 9 i \sqrt{42} (5 i \sqrt{6})$ .

Tap for more steps...

Step 7.1

Multiply $5$ by $- 9$ .

$- 45 i \sqrt{42} (i \sqrt{6})$

Step 7.2

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

$- 45 (i^{1} i) \sqrt{42} \sqrt{6}$

Step 7.3

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

$- 45 (i^{1} i^{1}) \sqrt{42} \sqrt{6}$

Step 7.4

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

$- 45 i^{1 + 1} \sqrt{42} \sqrt{6}$

Step 7.5

Add $1$ and $1$ .

$- 45 i^{2} \sqrt{42} \sqrt{6}$

Step 7.6

Combine using the product rule for radicals.

$- 45 i^{2} \sqrt{6 \cdot 42}$

Step 7.7

Multiply $6$ by $42$ .

$- 45 i^{2} \sqrt{252}$

Step 8

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

$- 45 \cdot - 1 \sqrt{252}$

Step 9

Multiply $- 45$ by $- 1$ .

$45 \sqrt{252}$

Step 10

Rewrite $252$ as $6^{2} \cdot 7$ .

Tap for more steps...

Step 10.1

Factor $36$ out of $252$ .

$45 \sqrt{36 (7)}$

Step 10.2

Rewrite $36$ as $6^{2}$ .

$45 \sqrt{6^{2} \cdot 7}$

Step 11

Pull terms out from under the radical.

$45 (| 6 | \sqrt{7})$

Step 12

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$45 (6 \sqrt{7})$

Step 13

Multiply $6$ by $45$ .

$270 \sqrt{7}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$270 \sqrt{7}$

Decimal Form:

$714.35285398 \dots$