Simplify 15 square root of 2*-2 square root of 20

$15 \sqrt{2} \cdot - 2 \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$15 \sqrt{2} \cdot (- 2 \sqrt{4 (5)})$

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

$15 \sqrt{2} \cdot (- 2 \sqrt{2^{2} \cdot 5})$

$15 \sqrt{2} \cdot (- 2 \sqrt{2^{2} \cdot 5})$

Pull terms out from under the radical.

$15 \sqrt{2} \cdot (- 2 (2 \sqrt{5}))$

Multiply $2$ by $- 2$ .

$15 \sqrt{2} \cdot (- 4 \sqrt{5})$

Multiply $15 \sqrt{2} (- 4 \sqrt{5})$ .

Multiply $- 4$ by $15$ .

$- 60 \sqrt{2} \sqrt{5}$

Combine using the product rule for radicals.

$- 60 \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$- 60 \sqrt{10}$

$- 60 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$- 60 \sqrt{10}$

Decimal Form:

$- 189.73665961 \dots$

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