Simplify the Radical Expression -3 square root of 5* square root of 20

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

Step 1

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 4

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

Multiply $2$ by $- 3$ .

$- 6 \sqrt{5} \sqrt{5}$

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

$- 6 ({\sqrt{5}}^{1} \sqrt{5})$

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

$- 6 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$- 6 {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

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

Step 5

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

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

$- 6 {(5^{\frac{1}{2}})}^{2}$

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

$- 6 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$- 6 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$- 6 \cdot 5^{1}$

Evaluate the exponent.

$- 6 \cdot 5$

Step 6

Multiply $- 6$ by $5$ .

$- 30$