Simplify - square root of 2( square root of 8+ square root of 32)

$- \sqrt{2} (\sqrt{8} + \sqrt{32})$

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$- \sqrt{2} (\sqrt{4 (2)} + \sqrt{32})$

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

$- \sqrt{2} (\sqrt{2^{2} \cdot 2} + \sqrt{32})$

Pull terms out from under the radical.

$- \sqrt{2} (2 \sqrt{2} + \sqrt{32})$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$- \sqrt{2} (2 \sqrt{2} + \sqrt{16 (2)})$

Rewrite $16$ as $4^{2}$ .

$- \sqrt{2} (2 \sqrt{2} + \sqrt{4^{2} \cdot 2})$

Pull terms out from under the radical.

$- \sqrt{2} (2 \sqrt{2} + 4 \sqrt{2})$

Add $2 \sqrt{2}$ and $4 \sqrt{2}$ .

$- \sqrt{2} (6 \sqrt{2})$

Multiply $- \sqrt{2} (6 \sqrt{2})$ .

Multiply $6$ by $- 1$ .

$- 6 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$- 6 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$- 6 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$- 6 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$- 6 {\sqrt{2}}^{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 6 {(2^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 6 \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$- 6 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 6 \cdot 2^{1}$

Evaluate the exponent.

$- 6 \cdot 2$

Multiply $- 6$ by $2$ .

$- 12$