Simplify 5 square root of 6x*2 square root of 8x^6

$5 \sqrt{6 x} \cdot 2 \sqrt{8 x^{6}}$

Rewrite $8 x^{6}$ as ${(2 x^{3})}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$5 \sqrt{6 x} \cdot (2 \sqrt{2^{2} \cdot 2 {(x^{3})}^{2}})$

Move $2$ .

$5 \sqrt{6 x} \cdot (2 \sqrt{2^{2} {(x^{3})}^{2} \cdot 2})$

Rewrite $2^{2} {(x^{3})}^{2}$ as ${(2 x^{3})}^{2}$ .

$5 \sqrt{6 x} \cdot (2 \sqrt{{(2 x^{3})}^{2} \cdot 2})$

Pull terms out from under the radical.

$5 \sqrt{6 x} \cdot (2 (2 x^{3} \sqrt{2}))$

Multiply $2$ by $2$ .

$5 \sqrt{6 x} \cdot (4 (x^{3} \sqrt{2}))$

Multiply $5 \sqrt{6 x} (4 x^{3} \sqrt{2})$ .

Multiply $4$ by $5$ .

$20 \sqrt{6 x} (x^{3} \sqrt{2})$

Combine using the product rule for radicals.

$20 (x^{3} \sqrt{6 x \cdot 2})$

Multiply $2$ by $6$ .

$20 (x^{3} \sqrt{12 x})$

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$20 (x^{3} \sqrt{4 (3) x})$

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

$20 (x^{3} \sqrt{2^{2} \cdot 3 x})$

Add parentheses.

$20 (x^{3} \sqrt{2^{2} \cdot (3 x)})$

Pull terms out from under the radical.

$20 (x^{3} (2 \sqrt{3 x}))$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$20 (2 x^{3} \sqrt{3 x})$

Multiply $2$ by $20$ .

$40 x^{3} \sqrt{3 x}$