Simplify the Radical Expression (7 square root of 6)(-5 square root of 30)

$(7 \sqrt{6}) (- 5 \sqrt{30})$

Step 1

Multiply $(7 \sqrt{6}) (- 5 \sqrt{30})$ .

Multiply $- 5$ by $7$ .

$- 35 \sqrt{6} \sqrt{30}$

Combine using the product rule for radicals.

$- 35 \sqrt{30 \cdot 6}$

Multiply $30$ by $6$ .

$- 35 \sqrt{180}$

Step 2

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$- 35 \sqrt{36 (5)}$

Rewrite $36$ as $6^{2}$ .

$- 35 \sqrt{6^{2} \cdot 5}$

Step 3

Pull terms out from under the radical.

$- 35 (| 6 | \sqrt{5})$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$- 35 (6 \sqrt{5})$

Step 5

Multiply $6$ by $- 35$ .

$- 210 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 210 \sqrt{5}$

Decimal Form:

$- 469.57427527 \dots$