Simplify the Radical Expression square root of 3*7 square root of 30

$\sqrt{3} \cdot 7 \sqrt{30}$

Step 1

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

$7 \cdot \sqrt{3} \sqrt{30}$

Step 2

Multiply $7 \sqrt{3} \sqrt{30}$ .

Combine using the product rule for radicals.

$7 \sqrt{30 \cdot 3}$

Multiply $30$ by $3$ .

$7 \sqrt{90}$

Step 3

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$7 \sqrt{9 (10)}$

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

$7 \sqrt{3^{2} \cdot 10}$

Step 4

Pull terms out from under the radical.

$7 (| 3 | \sqrt{10})$

Step 5

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

$7 (3 \sqrt{10})$

Step 6

Multiply $3$ by $7$ .

$21 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$21 \sqrt{10}$

Decimal Form:

$66.40783086 \dots$