Precalculus Examples

$\sqrt{5 x} - 6 \sqrt{20 x} + 3 \sqrt{180 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $20$ .

$\sqrt{5 x} - 6 \sqrt{4 (5) x} + 3 \sqrt{180 x}$

Step 1.1.2

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

$\sqrt{5 x} - 6 \sqrt{2^{2} \cdot 5 x} + 3 \sqrt{180 x}$

Step 1.1.3

Add parentheses.

$\sqrt{5 x} - 6 \sqrt{2^{2} \cdot (5 x)} + 3 \sqrt{180 x}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{5 x} - 6 (2 \sqrt{5 x}) + 3 \sqrt{180 x}$

Step 1.3

Multiply $2$ by $- 6$ .

$\sqrt{5 x} - 12 \sqrt{5 x} + 3 \sqrt{180 x}$

Step 1.4

Rewrite $180 x$ as $6^{2} \cdot (5 x)$ .

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Step 1.4.1

Factor $36$ out of $180$ .

$\sqrt{5 x} - 12 \sqrt{5 x} + 3 \sqrt{36 (5) x}$

Step 1.4.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{5 x} - 12 \sqrt{5 x} + 3 \sqrt{6^{2} \cdot 5 x}$

Step 1.4.3

Add parentheses.

$\sqrt{5 x} - 12 \sqrt{5 x} + 3 \sqrt{6^{2} \cdot (5 x)}$

Step 1.5

Pull terms out from under the radical.

$\sqrt{5 x} - 12 \sqrt{5 x} + 3 (6 \sqrt{5 x})$

Step 1.6

Multiply $6$ by $3$ .

$\sqrt{5 x} - 12 \sqrt{5 x} + 18 \sqrt{5 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 \sqrt{5 x}$ from $\sqrt{5 x}$ .

$- 11 \sqrt{5 x} + 18 \sqrt{5 x}$

Step 2.2

Add $- 11 \sqrt{5 x}$ and $18 \sqrt{5 x}$ .

$7 \sqrt{5 x}$