Simplify - square root of 54a^2b+ square root of 24a^2b

$- \sqrt{54 a^{2} b} + \sqrt{24 a^{2} b}$

Step 1

Simplify each term.

Rewrite $54 a^{2} b$ as ${(3 a)}^{2} \cdot (6 b)$ .

Factor $9$ out of $54$ .

$- \sqrt{9 (6) a^{2} b} + \sqrt{24 a^{2} b}$

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

$- \sqrt{3^{2} \cdot 6 a^{2} b} + \sqrt{24 a^{2} b}$

Move $6$ .

$- \sqrt{3^{2} a^{2} \cdot 6 b} + \sqrt{24 a^{2} b}$

Rewrite $3^{2} a^{2}$ as ${(3 a)}^{2}$ .

$- \sqrt{{(3 a)}^{2} \cdot 6 b} + \sqrt{24 a^{2} b}$

Add parentheses.

$- \sqrt{{(3 a)}^{2} \cdot (6 b)} + \sqrt{24 a^{2} b}$

Pull terms out from under the radical.

$- (3 a \sqrt{6 b}) + \sqrt{24 a^{2} b}$

Multiply $3$ by $- 1$ .

$- 3 (a \sqrt{6 b}) + \sqrt{24 a^{2} b}$

Rewrite $24 a^{2} b$ as ${(2 a)}^{2} \cdot (6 b)$ .

Factor $4$ out of $24$ .

$- 3 a \sqrt{6 b} + \sqrt{4 (6) a^{2} b}$

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

$- 3 a \sqrt{6 b} + \sqrt{2^{2} \cdot 6 a^{2} b}$

Move $6$ .

$- 3 a \sqrt{6 b} + \sqrt{2^{2} a^{2} \cdot 6 b}$

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

$- 3 a \sqrt{6 b} + \sqrt{{(2 a)}^{2} \cdot 6 b}$

Add parentheses.

$- 3 a \sqrt{6 b} + \sqrt{{(2 a)}^{2} \cdot (6 b)}$

Pull terms out from under the radical.

$- 3 a \sqrt{6 b} + 2 a \sqrt{6 b}$

Step 2

Add $- 3 a \sqrt{6 b}$ and $2 a \sqrt{6 b}$ .

$- a \sqrt{6 b}$