Simplify (7 square root of -10)(-8 square root of -7)

$(7 \sqrt{- 10}) (- 8 \sqrt{- 7})$

Step 1

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

$7 \sqrt{- 1 (10)} (- 8 \sqrt{- 7})$

Step 2

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

$7 (\sqrt{- 1} \cdot \sqrt{10}) (- 8 \sqrt{- 7})$

Step 3

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

$7 (i \cdot \sqrt{10}) (- 8 \sqrt{- 7})$

Step 4

Rewrite $- 7$ as $- 1 (7)$ .

$7 (i \cdot \sqrt{10}) (- 8 \sqrt{- 1 (7)})$

Step 5

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$7 (i \cdot \sqrt{10}) (- 8 (\sqrt{- 1} \cdot \sqrt{7}))$

Step 6

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

$7 (i \cdot \sqrt{10}) (- 8 (i \cdot \sqrt{7}))$

Step 7

Multiply $7 i \sqrt{10} (- 8 i \sqrt{7})$ .

Multiply $- 8$ by $7$ .

$- 56 i \sqrt{10} (i \sqrt{7})$

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

$- 56 (i^{1} i) \sqrt{10} \sqrt{7}$

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

$- 56 (i^{1} i^{1}) \sqrt{10} \sqrt{7}$

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

$- 56 i^{1 + 1} \sqrt{10} \sqrt{7}$

Add $1$ and $1$ .

$- 56 i^{2} \sqrt{10} \sqrt{7}$

Combine using the product rule for radicals.

$- 56 i^{2} \sqrt{7 \cdot 10}$

Multiply $7$ by $10$ .

$- 56 i^{2} \sqrt{70}$

Step 8

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

$- 56 \cdot - 1 \sqrt{70}$

Step 9

Multiply $- 56$ by $- 1$ .

$56 \sqrt{70}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$56 \sqrt{70}$

Decimal Form:

$468.52961485 \dots$

Simplify (7 square root of -10)(-8 square root of -7)

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