Simplify the Radical Expression square root of 6*7 square root of 18

$\sqrt{6} \cdot 7 \sqrt{18}$

Move $7$ to the left of $\sqrt{6}$ .

$7 \cdot \sqrt{6} \sqrt{18}$

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

Factor $9$ out of $18$ .

$7 \sqrt{6} \sqrt{9 (2)}$

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

$7 \sqrt{6} \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{6} (| 3 | \sqrt{2})$

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

$7 \sqrt{6} (3 \sqrt{2})$

Multiply $7 \sqrt{6} (3 \sqrt{2})$ .

Multiply $3$ by $7$ .

$21 \sqrt{6} \sqrt{2}$

Combine using the product rule for radicals.

$21 \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$21 \sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$21 \sqrt{4 (3)}$

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

$21 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$21 (| 2 | \sqrt{3})$

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

$21 (2 \sqrt{3})$

Multiply $2$ by $21$ .

$42 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$42 \sqrt{3}$

Decimal Form:

$72.74613391 \dots$