Simplify 2 square root of 5x^3(-3 square root of 10x^2)

$2 \sqrt{5 x^{3}} (- 3 \sqrt{10 x^{2}})$

Step 1

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

Factor out $x^{2}$ .

$2 \sqrt{5 (x^{2} x)} (- 3 \sqrt{10 x^{2}})$

Reorder $5$ and $x^{2}$ .

$2 \sqrt{x^{2} \cdot 5 x} (- 3 \sqrt{10 x^{2}})$

Add parentheses.

$2 \sqrt{x^{2} \cdot (5 x)} (- 3 \sqrt{10 x^{2}})$

$2 \sqrt{x^{2} \cdot (5 x)} (- 3 \sqrt{10 x^{2}})$

Step 2

Pull terms out from under the radical.

$2 (x \sqrt{5 x}) (- 3 \sqrt{10 x^{2}})$

Step 3

Reorder $10$ and $x^{2}$ .

$2 x \sqrt{5 x} (- 3 \sqrt{x^{2} \cdot 10})$

Step 4

Pull terms out from under the radical.

$2 x \sqrt{5 x} (- 3 (x \sqrt{10}))$

Step 5

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) \sqrt{5 x} (- 3 (\sqrt{10}))$

Multiply $x$ by $x$ .

$2 x^{2} \sqrt{5 x} (- 3 (\sqrt{10}))$

$2 x^{2} \sqrt{5 x} (- 3 (\sqrt{10}))$

Step 6

Multiply $2 x^{2} \sqrt{5 x} (- 3 \sqrt{10})$ .

Multiply $- 3$ by $2$ .

$- 6 x^{2} \sqrt{5 x} \sqrt{10}$

Combine using the product rule for radicals.

$- 6 x^{2} \sqrt{10 (5 x)}$

Multiply $10$ by $5$ .

$- 6 x^{2} \sqrt{50 x}$

$- 6 x^{2} \sqrt{50 x}$

Step 7

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$- 6 x^{2} \sqrt{25 (2) x}$

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

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

Add parentheses.

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Multiply $5$ by $- 6$ .

$- 30 x^{2} \sqrt{2 x}$

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