Simplify -3x^3 square root of 5+6 square root of 125x^6

$- 3 x^{3} \sqrt{5} + 6 \sqrt{125 x^{6}}$

Simplify each term.

Rewrite $125 x^{6}$ as ${(5 x^{3})}^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$- 3 x^{3} \sqrt{5} + 6 \sqrt{25 (5) x^{6}}$

Rewrite $25$ as $5^{2}$ .

$- 3 x^{3} \sqrt{5} + 6 \sqrt{5^{2} \cdot 5 x^{6}}$

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

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

Move $5$ .

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

Rewrite $5^{2} {(x^{3})}^{2}$ as ${(5 x^{3})}^{2}$ .

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

Pull terms out from under the radical.

$- 3 x^{3} \sqrt{5} + 6 (5 x^{3} \sqrt{5})$

Multiply $5$ by $6$ .

$- 3 x^{3} \sqrt{5} + 30 x^{3} \sqrt{5}$

Add $- 3 x^{3} \sqrt{5}$ and $30 x^{3} \sqrt{5}$ .

$27 x^{3} \sqrt{5}$