Simplify square root of 180*2 square root of 30

$\sqrt{180} \cdot 2 \sqrt{30}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5)} \cdot (2 \sqrt{30})$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 5} \cdot (2 \sqrt{30})$

$\sqrt{6^{2} \cdot 5} \cdot (2 \sqrt{30})$

Pull terms out from under the radical.

$6 \sqrt{5} \cdot (2 \sqrt{30})$

Multiply $6 \sqrt{5} (2 \sqrt{30})$ .

Multiply $2$ by $6$ .

$12 \sqrt{5} \sqrt{30}$

Combine using the product rule for radicals.

$12 \sqrt{30 \cdot 5}$

Multiply $30$ by $5$ .

$12 \sqrt{150}$

$12 \sqrt{150}$

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$12 \sqrt{25 (6)}$

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

$12 \sqrt{5^{2} \cdot 6}$

$12 \sqrt{5^{2} \cdot 6}$

Pull terms out from under the radical.

$12 (5 \sqrt{6})$

Multiply $5$ by $12$ .

$60 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{6}$

Decimal Form:

$146.96938456 \dots$

Related Questions