Simplify square root of 2n^2* square root of 30n

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

Step 1

Reorder $2$ and $n^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $n \sqrt{2} \sqrt{30 n}$ .

Combine using the product rule for radicals.

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

Multiply $2$ by $30$ .

$n \sqrt{60 n}$

Step 4

Rewrite $60 n$ as $2^{2} \cdot (15 n)$ .

Factor $4$ out of $60$ .

$n \sqrt{4 (15) n}$

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

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

Add parentheses.

$n \sqrt{2^{2} \cdot (15 n)}$

Step 5

Pull terms out from under the radical.

$n (2 \sqrt{15 n})$

Step 6

Rewrite using the commutative property of multiplication.

$2 n \sqrt{15 n}$