Simplify square root of -18( square root of -5- square root of 7)

$\sqrt{- 18} (\sqrt{- 5} - \sqrt{7})$

Rewrite $- 18$ as $- 1 (18)$ .

$\sqrt{- 1 (18)} (\sqrt{- 5} - \sqrt{7})$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\sqrt{- 1} \cdot \sqrt{18} (\sqrt{- 5} - \sqrt{7})$

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

$i \cdot \sqrt{18} (\sqrt{- 5} - \sqrt{7})$

Rewrite $- 5$ as $- 1 (5)$ .

$i \cdot \sqrt{18} (\sqrt{- 1 (5)} - \sqrt{7})$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$i \cdot \sqrt{18} (\sqrt{- 1} \cdot \sqrt{5} - \sqrt{7})$

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

$i \cdot \sqrt{18} (i \cdot \sqrt{5} - \sqrt{7})$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} (i \cdot \sqrt{5} - \sqrt{7})$

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

$i \cdot \sqrt{3^{2} \cdot 2} (i \cdot \sqrt{5} - \sqrt{7})$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) (i \cdot \sqrt{5} - \sqrt{7})$

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

$3 \cdot i \sqrt{2} (i \cdot \sqrt{5} - \sqrt{7})$

Apply the distributive property.

$3 i \sqrt{2} (i \sqrt{5}) + 3 i \sqrt{2} (- \sqrt{7})$

Multiply $3 i \sqrt{2} (i \sqrt{5})$ .

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

$3 (i^{1} i) \sqrt{2} \sqrt{5} + 3 i \sqrt{2} (- \sqrt{7})$

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

$3 (i^{1} i^{1}) \sqrt{2} \sqrt{5} + 3 i \sqrt{2} (- \sqrt{7})$

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

$3 i^{1 + 1} \sqrt{2} \sqrt{5} + 3 i \sqrt{2} (- \sqrt{7})$

Add $1$ and $1$ .

$3 i^{2} \sqrt{2} \sqrt{5} + 3 i \sqrt{2} (- \sqrt{7})$

Combine using the product rule for radicals.

$3 i^{2} \sqrt{5 \cdot 2} + 3 i \sqrt{2} (- \sqrt{7})$

Multiply $5$ by $2$ .

$3 i^{2} \sqrt{10} + 3 i \sqrt{2} (- \sqrt{7})$

Multiply $3 i \sqrt{2} (- \sqrt{7})$ .

Multiply $- 1$ by $3$ .

$3 i^{2} \sqrt{10} - 3 i \sqrt{2} \sqrt{7}$

Combine using the product rule for radicals.

$3 i^{2} \sqrt{10} - 3 i \sqrt{7 \cdot 2}$

Multiply $7$ by $2$ .

$3 i^{2} \sqrt{10} - 3 i \sqrt{14}$

Simplify each term.

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

$3 \cdot - 1 \sqrt{10} - 3 i \sqrt{14}$

Multiply $3$ by $- 1$ .

$- 3 \sqrt{10} - 3 i \sqrt{14}$

Simplify square root of -18( square root of -5- square root of 7)

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