Simplify the Radical Expression 5 square root of 20*3 square root of 8

$5 \sqrt{20} \cdot 3 \sqrt{8}$

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

Factor $4$ out of $20$ .

$5 \sqrt{4 (5)} \cdot 3 \sqrt{8}$

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

$5 \sqrt{2^{2} \cdot 5} \cdot 3 \sqrt{8}$

Pull terms out from under the radical.

$5 (| 2 | \sqrt{5}) \cdot 3 \sqrt{8}$

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

$5 (2 \sqrt{5}) \cdot 3 \sqrt{8}$

Multiply $2$ by $5$ .

$10 \sqrt{5} \cdot 3 \sqrt{8}$

Multiply $3$ by $10$ .

$30 \sqrt{5} \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$30 \sqrt{5} \sqrt{4 (2)}$

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

$30 \sqrt{5} \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$30 \sqrt{5} (| 2 | \sqrt{2})$

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

$30 \sqrt{5} (2 \sqrt{2})$

Multiply $30 \sqrt{5} (2 \sqrt{2})$ .

Multiply $2$ by $30$ .

$60 \sqrt{5} \sqrt{2}$

Combine using the product rule for radicals.

$60 \sqrt{2 \cdot 5}$

Multiply $2$ by $5$ .

$60 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{10}$

Decimal Form:

$189.73665961 \dots$