Evaluate -8 square root of 128+ square root of 128- fourth root of 96

$- 8 \sqrt{128} + \sqrt{128} - \sqrt[4]{96}$

Step 1

Simplify each term.

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$- 8 \sqrt{64 (2)} + \sqrt{128} - \sqrt[4]{96}$

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

$- 8 \sqrt{8^{2} \cdot 2} + \sqrt{128} - \sqrt[4]{96}$

Pull terms out from under the radical.

$- 8 (8 \sqrt{2}) + \sqrt{128} - \sqrt[4]{96}$

Multiply $8$ by $- 8$ .

$- 64 \sqrt{2} + \sqrt{128} - \sqrt[4]{96}$

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$- 64 \sqrt{2} + \sqrt{64 (2)} - \sqrt[4]{96}$

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

$- 64 \sqrt{2} + \sqrt{8^{2} \cdot 2} - \sqrt[4]{96}$

Pull terms out from under the radical.

$- 64 \sqrt{2} + 8 \sqrt{2} - \sqrt[4]{96}$

Rewrite $96$ as $2^{4} \cdot 6$ .

Factor $16$ out of $96$ .

$- 64 \sqrt{2} + 8 \sqrt{2} - \sqrt[4]{16 (6)}$

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

$- 64 \sqrt{2} + 8 \sqrt{2} - \sqrt[4]{2^{4} \cdot 6}$

Pull terms out from under the radical.

$- 64 \sqrt{2} + 8 \sqrt{2} - (2 \sqrt[4]{6})$

Multiply $2$ by $- 1$ .

$- 64 \sqrt{2} + 8 \sqrt{2} - 2 \sqrt[4]{6}$

Step 2

Add $- 64 \sqrt{2}$ and $8 \sqrt{2}$ .

$- 56 \sqrt{2} - 2 \sqrt[4]{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 56 \sqrt{2} - 2 \sqrt[4]{6}$

Decimal Form:

$- 82.32612865 \dots$