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

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

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

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Multiply $- 5$ by $7$ .

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

Combine using the product rule for radicals.

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

Multiply $30$ by $6$ .

$- 35 \sqrt{180}$

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

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Factor $36$ out of $180$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Multiply $6$ by $- 35$ .

$- 210 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$- 210 \sqrt{5}$

Decimal Form:

$- 469.57427527 \dots$

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

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