Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Factor $9$ out of $45$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add parentheses.

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

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

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Step 2.3.1

Factor $4$ out of $20$ .

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

Step 2.3.2

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

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

Step 2.3.3

Add parentheses.

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

Step 2.4

Pull terms out from under the radical.

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

Step 2.5

Multiply $2$ by $4$ .

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

Step 2.6

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

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Step 2.6.1

Factor $25$ out of $125$ .

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

Step 2.6.2

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

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

Step 2.6.3

Add parentheses.

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

Step 2.7

Pull terms out from under the radical.

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

Step 2.8

Multiply $5$ by $- 2$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

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

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

Step 3.2

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

$\sqrt{5 b}$