Algebra Examples

$(4 \sqrt{- 72}) (- 4 \sqrt{- 64})$

Step 1

Rewrite $- 72$ as $- 1 (72)$ .

$4 \sqrt{- 1 (72)} (- 4 \sqrt{- 64})$

Step 2

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$4 (\sqrt{- 1} \cdot \sqrt{72}) (- 4 \sqrt{- 64})$

Step 3

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

$4 (i \cdot \sqrt{72}) (- 4 \sqrt{- 64})$

Step 4

Rewrite $- 64$ as $- 1 (64)$ .

$4 (i \cdot \sqrt{72}) (- 4 \sqrt{- 1 (64)})$

Step 5

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$4 (i \cdot \sqrt{72}) (- 4 (\sqrt{- 1} \cdot \sqrt{64}))$

Step 6

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

$4 (i \cdot \sqrt{72}) (- 4 (i \cdot \sqrt{64}))$

Step 7

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 7.1

Factor $36$ out of $72$ .

$4 (i \cdot \sqrt{36 (2)}) (- 4 (i \cdot \sqrt{64}))$

Step 7.2

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

$4 (i \cdot \sqrt{6^{2} \cdot 2}) (- 4 (i \cdot \sqrt{64}))$

Step 8

Pull terms out from under the radical.

$4 (i \cdot (6 \sqrt{2})) (- 4 (i \cdot \sqrt{64}))$

Step 9

Simplify the expression.

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Step 9.1

Move $6$ to the left of $i$ .

$4 (6 \cdot i \sqrt{2}) (- 4 (i \cdot \sqrt{64}))$

Step 9.2

Multiply $6$ by $4$ .

$24 (i \sqrt{2}) (- 4 (i \cdot \sqrt{64}))$

Step 9.3

Rewrite $64$ as $8^{2}$ .

$24 i \sqrt{2} (- 4 (i \cdot \sqrt{8^{2}}))$

Step 9.4

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

$24 i \sqrt{2} (- 4 (i \cdot 8))$

Step 9.5

Move $8$ to the left of $i$ .

$24 i \sqrt{2} (- 4 (8 \cdot i))$

Step 9.6

Multiply $8$ by $- 4$ .

$24 i \sqrt{2} (- 32 i)$

Step 10

Multiply $24 i \sqrt{2} (- 32 i)$ .

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Step 10.1

Multiply $- 32$ by $24$ .

$- 768 i \sqrt{2} i$

Step 10.2

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

$- 768 (i^{1} i) \sqrt{2}$

Step 10.3

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

$- 768 (i^{1} i^{1}) \sqrt{2}$

Step 10.4

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

$- 768 i^{1 + 1} \sqrt{2}$

Step 10.5

Add $1$ and $1$ .

$- 768 i^{2} \sqrt{2}$

Step 11

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

$- 768 \cdot - 1 \sqrt{2}$

Step 12

Multiply $- 768$ by $- 1$ .

$768 \sqrt{2}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$768 \sqrt{2}$

Decimal Form:

$1086.11601590 \dots$