Calculus Examples

$(5 i \sqrt{- 6}) (7 \sqrt{- 10})$

Step 1

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

$5 i \sqrt{- 1 (6)} (7 \sqrt{- 10})$

Step 2

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

$5 i (\sqrt{- 1} \cdot \sqrt{6}) (7 \sqrt{- 10})$

Step 3

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

$5 i (i \cdot \sqrt{6}) (7 \sqrt{- 10})$

Step 4

Rewrite $- 10$ as $- 1 (10)$ .

$5 i (i \cdot \sqrt{6}) (7 \sqrt{- 1 (10)})$

Step 5

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$5 i (i \cdot \sqrt{6}) (7 (\sqrt{- 1} \cdot \sqrt{10}))$

Step 6

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

$5 i (i \cdot \sqrt{6}) (7 (i \cdot \sqrt{10}))$

Step 7

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

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Step 7.1

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

$5 (i^{1} i) \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 7.2

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

$5 (i^{1} i^{1}) \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 7.3

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

$5 i^{1 + 1} \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 7.4

Add $1$ and $1$ .

$5 i^{2} \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 8

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

$5 \cdot - 1 \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 9

Multiply $5$ by $- 1$ .

$- 5 \sqrt{6} (7 (i \cdot \sqrt{10}))$

Step 10

Multiply $- 5 \sqrt{6} (7 i \sqrt{10})$ .

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Step 10.1

Multiply $7$ by $- 5$ .

$- 35 \sqrt{6} (i \sqrt{10})$

Step 10.2

Combine using the product rule for radicals.

$- 35 \sqrt{10 \cdot 6} i$

Step 10.3

Multiply $10$ by $6$ .

$- 35 \sqrt{60} i$

Step 11

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 11.1

Factor $4$ out of $60$ .

$- 35 \sqrt{4 (15)} i$

Step 11.2

Rewrite $4$ as $2^{2}$ .

$- 35 \sqrt{2^{2} \cdot 15} i$

Step 12

Pull terms out from under the radical.

$- 35 (2 \sqrt{15}) i$

Step 13

Multiply $2$ by $- 35$ .

$- 70 \sqrt{15} i$