Simplify the Radical Expression square root of 3*7 square root of 6

$\sqrt{3} \cdot 7 \sqrt{6}$

Move $7$ to the left of $\sqrt{3}$ .

$7 \cdot \sqrt{3} \sqrt{6}$

Multiply $7 \sqrt{3} \sqrt{6}$ .

Combine using the product rule for radicals.

$7 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$7 \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$7 \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$7 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$7 (| 3 | \sqrt{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$7 (3 \sqrt{2})$

Multiply $3$ by $7$ .

$21 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$21 \sqrt{2}$

Decimal Form:

$29.69848480 \dots$