Simplify 3 square root of 6*5 square root of 12

$3 \sqrt{6} \cdot 5 \sqrt{12}$

Step 1

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

Factor $4$ out of $12$ .

$3 \sqrt{6} \cdot (5 \sqrt{4 (3)})$

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

$3 \sqrt{6} \cdot (5 \sqrt{2^{2} \cdot 3})$

$3 \sqrt{6} \cdot (5 \sqrt{2^{2} \cdot 3})$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $5$ .

$3 \sqrt{6} \cdot (10 \sqrt{3})$

Step 4

Multiply $3 \sqrt{6} (10 \sqrt{3})$ .

Multiply $10$ by $3$ .

$30 \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$30 \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$30 \sqrt{18}$

$30 \sqrt{18}$

Step 5

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

Factor $9$ out of $18$ .

$30 \sqrt{9 (2)}$

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

$30 \sqrt{3^{2} \cdot 2}$

$30 \sqrt{3^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$30 (3 \sqrt{2})$

Step 7

Multiply $3$ by $30$ .

$90 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$90 \sqrt{2}$

Decimal Form:

$127.27922061 \dots$

Related Questions