Simplify the Radical Expression 2 square root of 53 square root of 2 square root of 6

$2 \sqrt{5} \cdot 3 \sqrt{2} \cdot \sqrt{6}$

Multiply $3$ by $2$ .

$6 \sqrt{5} \sqrt{2} \cdot \sqrt{6}$

Multiply $6 \sqrt{5} \sqrt{2}$ .

Combine using the product rule for radicals.

$6 \sqrt{2 \cdot 5} \cdot \sqrt{6}$

Multiply $2$ by $5$ .

$6 \sqrt{10} \cdot \sqrt{6}$

Multiply $6 \sqrt{10} \sqrt{6}$ .

Combine using the product rule for radicals.

$6 \sqrt{6 \cdot 10}$

Multiply $6$ by $10$ .

$6 \sqrt{60}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$6 \sqrt{4 (15)}$

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

$6 \sqrt{2^{2} \cdot 15}$

Pull terms out from under the radical.

$6 (| 2 | \sqrt{15})$

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

$6 (2 \sqrt{15})$

Multiply $2$ by $6$ .

$12 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{15}$

Decimal Form:

$46.47580015 \dots$

Simplify the Radical Expression 2 square root of 5*3 square root of 2* square root of 6