Simplify (-5 square root of 6)(2 square root of 3)

$(- 5 \sqrt{6}) (2 \sqrt{3})$

Step 1

Multiply $(- 5 \sqrt{6}) (2 \sqrt{3})$ .

Multiply $2$ by $- 5$ .

$- 10 \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$- 10 \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$- 10 \sqrt{18}$

$- 10 \sqrt{18}$

Step 2

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$- 10 \sqrt{9 (2)}$

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

$- 10 \sqrt{3^{2} \cdot 2}$

$- 10 \sqrt{3^{2} \cdot 2}$

Step 3

Pull terms out from under the radical.

$- 10 (3 \sqrt{2})$

Step 4

Multiply $3$ by $- 10$ .

$- 30 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 30 \sqrt{2}$

Decimal Form:

$- 42.42640687 \dots$

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