Simplify 3 square root of 6*5 square root of 2

$3 \sqrt{6} \cdot 5 \sqrt{2}$

Step 1

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

Multiply $5$ by $3$ .

$15 \sqrt{6} \sqrt{2}$

Combine using the product rule for radicals.

$15 \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$15 \sqrt{12}$

$15 \sqrt{12}$

Step 2

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$15 \sqrt{4 (3)}$

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

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

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

Step 3

Pull terms out from under the radical.

$15 (2 \sqrt{3})$

Step 4

Multiply $2$ by $15$ .

$30 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{3}$

Decimal Form:

$51.96152422 \dots$

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