Simplify the Radical Expression 6 square root of 10*7 square root of 20

$6 \sqrt{10} \cdot 7 \sqrt{20}$

Multiply $7$ by $6$ .

$42 \sqrt{10} \sqrt{20}$

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

Factor $4$ out of $20$ .

$42 \sqrt{10} \sqrt{4 (5)}$

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

$42 \sqrt{10} \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$42 \sqrt{10} (| 2 | \sqrt{5})$

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

$42 \sqrt{10} (2 \sqrt{5})$

Multiply $42 \sqrt{10} (2 \sqrt{5})$ .

Multiply $2$ by $42$ .

$84 \sqrt{10} \sqrt{5}$

Combine using the product rule for radicals.

$84 \sqrt{5 \cdot 10}$

Multiply $5$ by $10$ .

$84 \sqrt{50}$

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

Factor $25$ out of $50$ .

$84 \sqrt{25 (2)}$

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

$84 \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$84 (| 5 | \sqrt{2})$

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

$84 (5 \sqrt{2})$

Multiply $5$ by $84$ .

$420 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$420 \sqrt{2}$

Decimal Form:

$593.96969619 \dots$