Simplify 3 square root of 5a*-3 square root of 20a^3

$3 \sqrt{5 a} \cdot - 3 \sqrt{20 a^{3}}$

Rewrite $20 a^{3}$ as ${(2 a)}^{2} \cdot (5 a)$ .

Factor $4$ out of $20$ .

$3 \sqrt{5 a} \cdot (- 3 \sqrt{4 (5) a^{3}})$

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

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

Factor out $a^{2}$ .

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

Move $5$ .

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

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

$3 \sqrt{5 a} \cdot (- 6 (a \sqrt{5 a}))$

Multiply $3 \sqrt{5 a} (- 6 a \sqrt{5 a})$ .

Multiply $- 6$ by $3$ .

$- 18 \sqrt{5 a} (a \sqrt{5 a})$

Raise $\sqrt{5 a}$ to the power of $1$ .

$- 18 (a ({\sqrt{5 a}}^{1} \sqrt{5 a}))$

Raise $\sqrt{5 a}$ to the power of $1$ .

$- 18 (a ({\sqrt{5 a}}^{1} {\sqrt{5 a}}^{1}))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 18 (a {\sqrt{5 a}}^{1 + 1})$

Add $1$ and $1$ .

$- 18 (a {\sqrt{5 a}}^{2})$

Rewrite ${\sqrt{5 a}}^{2}$ as $5 a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 a}$ as ${(5 a)}^{\frac{1}{2}}$ .

$- 18 (a {({(5 a)}^{\frac{1}{2}})}^{2})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 18 (a {(5 a)}^{\frac{1}{2} \cdot 2})$

Combine $\frac{1}{2}$ and $2$ .

$- 18 (a {(5 a)}^{\frac{2}{2}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 18 (a {(5 a)}^{\frac{2}{2}})$

Rewrite the expression.

$- 18 (a {(5 a)}^{1})$

Simplify.

$- 18 (a (5 a))$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$- 18 (a \cdot a \cdot 5)$

Multiply $a$ by $a$ .

$- 18 (a^{2} \cdot 5)$

Move $5$ to the left of $a^{2}$ .

$- 18 (5 \cdot a^{2})$

Multiply $5$ by $- 18$ .

$- 90 a^{2}$

Simplify 3 square root of 5a*-3 square root of 20a^3

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