Simplify the Radical Expression (-3 square root of 2)(-2 square root of 50)

$(- 3 \sqrt{2}) (- 2 \sqrt{50})$

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

Factor $25$ out of $50$ .

$- 3 \sqrt{2} (- 2 \sqrt{25 (2)})$

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

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

Pull terms out from under the radical.

$- 3 \sqrt{2} (- 2 (| 5 | \sqrt{2}))$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

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

Multiply $5$ by $- 2$ .

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

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

Multiply $- 10$ by $- 3$ .

$30 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$30 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$30 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$30 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

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

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

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

$30 {(2^{\frac{1}{2}})}^{2}$

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

$30 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$30 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$30 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$30 \cdot 2^{1}$

Evaluate the exponent.

$30 \cdot 2$

Multiply $30$ by $2$ .

$60$