Simplify square root of 5(2 square root of 6x- square root of 96x)

$\sqrt{5} (2 \sqrt{6 x} - \sqrt{96 x})$

Simplify each term.

Rewrite $96 x$ as ${(2^{2})}^{2} \cdot (6 x)$ .

Factor $16$ out of $96$ .

$\sqrt{5} (2 \sqrt{6 x} - \sqrt{16 (6) x})$

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

$\sqrt{5} (2 \sqrt{6 x} - \sqrt{4^{2} \cdot 6 x})$

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

$\sqrt{5} (2 \sqrt{6 x} - \sqrt{{(2^{2})}^{2} \cdot 6 x})$

Add parentheses.

$\sqrt{5} (2 \sqrt{6 x} - \sqrt{{(2^{2})}^{2} \cdot (6 x)})$

Pull terms out from under the radical.

$\sqrt{5} (2 \sqrt{6 x} - (2^{2} \sqrt{6 x}))$

Raise $2$ to the power of $2$ .

$\sqrt{5} (2 \sqrt{6 x} - (4 \sqrt{6 x}))$

Multiply $4$ by $- 1$ .

$\sqrt{5} (2 \sqrt{6 x} - 4 \sqrt{6 x})$

Subtract $4 \sqrt{6 x}$ from $2 \sqrt{6 x}$ .

$\sqrt{5} (- 2 \sqrt{6 x})$

Multiply $\sqrt{5} (- 2 \sqrt{6 x})$ .

Combine using the product rule for radicals.

$- 2 \sqrt{5 (6 x)}$

Multiply $5$ by $6$ .

$- 2 \sqrt{30 x}$