Simplify a square root of 125y-b square root of 45y

$a \sqrt{125 y} - b \sqrt{45 y}$

Step 1

Rewrite $125 y$ as $5^{2} \cdot (5 y)$ .

Factor $25$ out of $125$ .

$a \sqrt{25 (5) y} - b \sqrt{45 y}$

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

$a \sqrt{5^{2} \cdot 5 y} - b \sqrt{45 y}$

Add parentheses.

$a \sqrt{5^{2} \cdot (5 y)} - b \sqrt{45 y}$

Step 2

Pull terms out from under the radical.

$a (5 \sqrt{5 y}) - b \sqrt{45 y}$

Step 3

Rewrite using the commutative property of multiplication.

$5 a \sqrt{5 y} - b \sqrt{45 y}$

Step 4

Rewrite $45 y$ as $3^{2} \cdot (5 y)$ .

Factor $9$ out of $45$ .

$5 a \sqrt{5 y} - b \sqrt{9 (5) y}$

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

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $3$ by $- 1$ .

$5 a \sqrt{5 y} - 3 b \sqrt{5 y}$