Simplify the Radical Expression 3 square root of 7*7 square root of 14

$3 \sqrt{7} \cdot 7 \sqrt{14}$

Step 1

Multiply $7$ by $3$ .

$21 \sqrt{7} \sqrt{14}$

Step 2

Multiply $21 \sqrt{7} \sqrt{14}$ .

Combine using the product rule for radicals.

$21 \sqrt{14 \cdot 7}$

Multiply $14$ by $7$ .

$21 \sqrt{98}$

Step 3

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$21 \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$21 \sqrt{7^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$21 (| 7 | \sqrt{2})$

Step 5

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$21 (7 \sqrt{2})$

Step 6

Multiply $7$ by $21$ .

$147 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$147 \sqrt{2}$

Decimal Form:

$207.88939366 \dots$