Simplify (3 square root of 15)(-4 square root of 45)

$(3 \sqrt{15}) (- 4 \sqrt{45})$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$3 \sqrt{15} (- 4 \sqrt{9 (5)})$

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

$3 \sqrt{15} (- 4 \sqrt{3^{2} \cdot 5})$

$3 \sqrt{15} (- 4 \sqrt{3^{2} \cdot 5})$

Pull terms out from under the radical.

$3 \sqrt{15} (- 4 (3 \sqrt{5}))$

Multiply $3$ by $- 4$ .

$3 \sqrt{15} (- 12 \sqrt{5})$

Multiply $3 \sqrt{15} (- 12 \sqrt{5})$ .

Multiply $- 12$ by $3$ .

$- 36 \sqrt{15} \sqrt{5}$

Combine using the product rule for radicals.

$- 36 \sqrt{5 \cdot 15}$

Multiply $5$ by $15$ .

$- 36 \sqrt{75}$

$- 36 \sqrt{75}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$- 36 \sqrt{25 (3)}$

Rewrite $25$ as $5^{2}$ .

$- 36 \sqrt{5^{2} \cdot 3}$

$- 36 \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$- 36 (5 \sqrt{3})$

Multiply $5$ by $- 36$ .

$- 180 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- 180 \sqrt{3}$

Decimal Form:

$- 311.76914536 \dots$

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