Simplify the Radical Expression -3ab square root of 50a^2b^2

$- 3 a b \sqrt{50 a^{2} b^{2}}$

Step 1

Rewrite $50 a^{2} b^{2}$ as ${(5 a b)}^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$- 3 a b \sqrt{25 (2) a^{2} b^{2}}$

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

$- 3 a b \sqrt{5^{2} \cdot 2 a^{2} b^{2}}$

Move $2$ .

$- 3 a b \sqrt{5^{2} a^{2} b^{2} \cdot 2}$

Rewrite $5^{2} a^{2} b^{2}$ as ${(5 a b)}^{2}$ .

$- 3 a b \sqrt{{(5 a b)}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$- 3 a b (| 5 a b | \sqrt{2})$

Step 3

Remove non-negative terms from the absolute value.

$- 3 a b (5 | a b | \sqrt{2})$

Step 4

Multiply $5$ by $- 3$ .

$- 15 a b (| a b | \sqrt{2})$

Step 5

Reorder factors in $- 15 a b (| a b | \sqrt{2})$ .

$- 15 a b | a b | \sqrt{2}$