Simplify 8 square root of 64- square root of 96

$8 \sqrt{64} - \sqrt{96}$

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

$8 \sqrt{8^{2}} - \sqrt{96}$

Pull terms out from under the radical, assuming positive real numbers.

$8 \cdot 8 - \sqrt{96}$

Multiply $8$ by $8$ .

$64 - \sqrt{96}$

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

Factor $16$ out of $96$ .

$64 - \sqrt{16 (6)}$

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

$64 - \sqrt{4^{2} \cdot 6}$

Pull terms out from under the radical.

$64 - (4 \sqrt{6})$

Multiply $4$ by $- 1$ .

$64 - 4 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$64 - 4 \sqrt{6}$

Decimal Form:

$54.20204102 \dots$