Simplify ( square root of 45b+4 square root of 20b-2 square root of 125b)

$(\sqrt{45 b} + 4 \sqrt{20 b} - 2 \sqrt{125 b})$

Step 1

Remove parentheses.

$\sqrt{45 b} + 4 \sqrt{20 b} - 2 \sqrt{125 b}$

Step 2

Simplify each term.

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

Factor $9$ out of $45$ .

$\sqrt{9 (5) b} + 4 \sqrt{20 b} - 2 \sqrt{125 b}$

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

$\sqrt{3^{2} \cdot 5 b} + 4 \sqrt{20 b} - 2 \sqrt{125 b}$

Add parentheses.

$\sqrt{3^{2} \cdot (5 b)} + 4 \sqrt{20 b} - 2 \sqrt{125 b}$

Pull terms out from under the radical.

$3 \sqrt{5 b} + 4 \sqrt{20 b} - 2 \sqrt{125 b}$

Rewrite $20 b$ as $2^{2} \cdot (5 b)$ .

Factor $4$ out of $20$ .

$3 \sqrt{5 b} + 4 \sqrt{4 (5) b} - 2 \sqrt{125 b}$

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

$3 \sqrt{5 b} + 4 \sqrt{2^{2} \cdot 5 b} - 2 \sqrt{125 b}$

Add parentheses.

$3 \sqrt{5 b} + 4 \sqrt{2^{2} \cdot (5 b)} - 2 \sqrt{125 b}$

Pull terms out from under the radical.

$3 \sqrt{5 b} + 4 (2 \sqrt{5 b}) - 2 \sqrt{125 b}$

Multiply $2$ by $4$ .

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 2 \sqrt{125 b}$

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

Factor $25$ out of $125$ .

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 2 \sqrt{25 (5) b}$

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

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 2 \sqrt{5^{2} \cdot 5 b}$

Add parentheses.

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 2 \sqrt{5^{2} \cdot (5 b)}$

Pull terms out from under the radical.

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 2 (5 \sqrt{5 b})$

Multiply $5$ by $- 2$ .

$3 \sqrt{5 b} + 8 \sqrt{5 b} - 10 \sqrt{5 b}$

Step 3

Simplify by adding terms.

Add $3 \sqrt{5 b}$ and $8 \sqrt{5 b}$ .

$11 \sqrt{5 b} - 10 \sqrt{5 b}$

Subtract $10 \sqrt{5 b}$ from $11 \sqrt{5 b}$ .

$\sqrt{5 b}$