Algebra Examples

$(- 9 \sqrt{- 63}) (- \sqrt{- 49})$

Step 1

Rewrite $- 63$ as $- 1 (63)$ .

$- 9 \sqrt{- 1 (63)} (- \sqrt{- 49})$

Step 2

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$- 9 (\sqrt{- 1} \cdot \sqrt{63}) (- \sqrt{- 49})$

Step 3

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

$- 9 (i \cdot \sqrt{63}) (- \sqrt{- 49})$

Step 4

Rewrite $- 49$ as $- 1 (49)$ .

$- 9 (i \cdot \sqrt{63}) (- \sqrt{- 1 (49)})$

Step 5

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$- 9 (i \cdot \sqrt{63}) (- (\sqrt{- 1} \cdot \sqrt{49}))$

Step 6

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

$- 9 (i \cdot \sqrt{63}) (- (i \cdot \sqrt{49}))$

Step 7

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

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Step 7.1

Factor $9$ out of $63$ .

$- 9 (i \cdot \sqrt{9 (7)}) (- (i \cdot \sqrt{49}))$

Step 7.2

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

$- 9 (i \cdot \sqrt{3^{2} \cdot 7}) (- (i \cdot \sqrt{49}))$

Step 8

Pull terms out from under the radical.

$- 9 (i \cdot (3 \sqrt{7})) (- (i \cdot \sqrt{49}))$

Step 9

Simplify the expression.

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Step 9.1

Move $3$ to the left of $i$ .

$- 9 (3 \cdot i \sqrt{7}) (- (i \cdot \sqrt{49}))$

Step 9.2

Multiply $3$ by $- 9$ .

$- 27 (i \sqrt{7}) (- (i \cdot \sqrt{49}))$

Step 9.3

Rewrite $49$ as $7^{2}$ .

$- 27 i \sqrt{7} (- (i \cdot \sqrt{7^{2}}))$

Step 10

Pull terms out from under the radical, assuming positive real numbers.

$- 27 i \sqrt{7} (- (i \cdot 7))$

Step 11

Move $7$ to the left of $i$ .

$- 27 i \sqrt{7} (- (7 \cdot i))$

Step 12

Multiply $7$ by $- 1$ .

$- 27 i \sqrt{7} (- 7 i)$

Step 13

Multiply $- 27 i \sqrt{7} (- 7 i)$ .

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Step 13.1

Multiply $- 7$ by $- 27$ .

$189 i \sqrt{7} i$

Step 13.2

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

$189 (i^{1} i) \sqrt{7}$

Step 13.3

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

$189 (i^{1} i^{1}) \sqrt{7}$

Step 13.4

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

$189 i^{1 + 1} \sqrt{7}$

Step 13.5

Add $1$ and $1$ .

$189 i^{2} \sqrt{7}$

Step 14

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

$189 \cdot - 1 \sqrt{7}$

Step 15

Multiply $189$ by $- 1$ .

$- 189 \sqrt{7}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$- 189 \sqrt{7}$

Decimal Form:

$- 500.04699779 \dots$