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Simplify -6 square root of 15* square root of 12

$- 6 \sqrt{15} \cdot \sqrt{12}$

Step 1

Rewrite

$12$ as

$2^{2} \cdot 3$ .

Factor

$4$ out of

$12$ .

$- 6 \sqrt{15} \cdot \sqrt{4 (3)}$

Rewrite

$4$ as

$2^{2}$ .

$- 6 \sqrt{15} \cdot \sqrt{2^{2} \cdot 3}$

$- 6 \sqrt{15} \cdot \sqrt{2^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$- 6 \sqrt{15} \cdot (2 \sqrt{3})$

Step 3

Multiply

$- 6 \sqrt{15} (2 \sqrt{3})$ .

Multiply

$2$ by

$- 6$ .

$- 12 \sqrt{15} \sqrt{3}$

Combine using the product rule for radicals.

$- 12 \sqrt{3 \cdot 15}$

Multiply

$3$ by

$15$ .

$- 12 \sqrt{45}$

$- 12 \sqrt{45}$

Step 4

Rewrite

$45$ as

$3^{2} \cdot 5$ .

Factor

$9$ out of

$45$ .

$- 12 \sqrt{9 (5)}$

Rewrite

$9$ as

$3^{2}$ .

$- 12 \sqrt{3^{2} \cdot 5}$

$- 12 \sqrt{3^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply

$3$ by

$- 12$ .

$- 36 \sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- 36 \sqrt{5}$

Decimal Form:

$- 80.49844718 \dots$

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