Algebra Examples

$3 \sqrt{6 x^{2}} - 2 \sqrt{20 x^{3}} + 2 x \sqrt{45 x}$

Step 1

Simplify each term.

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Step 1.1

Reorder $6$ and $x^{2}$ .

$3 \sqrt{x^{2} \cdot 6} - 2 \sqrt{20 x^{3}} + 2 x \sqrt{45 x}$

Step 1.2

Pull terms out from under the radical.

$3 (x \sqrt{6}) - 2 \sqrt{20 x^{3}} + 2 x \sqrt{45 x}$

Step 1.3

Rewrite $20 x^{3}$ as ${(2 x)}^{2} \cdot (5 x)$ .

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Step 1.3.1

Factor $4$ out of $20$ .

$3 x \sqrt{6} - 2 \sqrt{4 (5) x^{3}} + 2 x \sqrt{45 x}$

Step 1.3.2

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

$3 x \sqrt{6} - 2 \sqrt{2^{2} \cdot 5 x^{3}} + 2 x \sqrt{45 x}$

Step 1.3.3

Factor out $x^{2}$ .

$3 x \sqrt{6} - 2 \sqrt{2^{2} \cdot 5 (x^{2} x)} + 2 x \sqrt{45 x}$

Step 1.3.4

Move $5$ .

$3 x \sqrt{6} - 2 \sqrt{2^{2} x^{2} \cdot 5 x} + 2 x \sqrt{45 x}$

Step 1.3.5

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

$3 x \sqrt{6} - 2 \sqrt{{(2 x)}^{2} \cdot 5 x} + 2 x \sqrt{45 x}$

Step 1.3.6

Add parentheses.

$3 x \sqrt{6} - 2 \sqrt{{(2 x)}^{2} \cdot (5 x)} + 2 x \sqrt{45 x}$

Step 1.4

Pull terms out from under the radical.

$3 x \sqrt{6} - 2 (2 x \sqrt{5 x}) + 2 x \sqrt{45 x}$

Step 1.5

Multiply $2$ by $- 2$ .

$3 x \sqrt{6} - 4 (x \sqrt{5 x}) + 2 x \sqrt{45 x}$

Step 1.6

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

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Step 1.6.1

Factor $9$ out of $45$ .

$3 x \sqrt{6} - 4 x \sqrt{5 x} + 2 x \sqrt{9 (5) x}$

Step 1.6.2

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

$3 x \sqrt{6} - 4 x \sqrt{5 x} + 2 x \sqrt{3^{2} \cdot 5 x}$

Step 1.6.3

Add parentheses.

$3 x \sqrt{6} - 4 x \sqrt{5 x} + 2 x \sqrt{3^{2} \cdot (5 x)}$

Step 1.7

Pull terms out from under the radical.

$3 x \sqrt{6} - 4 x \sqrt{5 x} + 2 x (3 \sqrt{5 x})$

Step 1.8

Multiply $3$ by $2$ .

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

Step 2

Add $- 4 x \sqrt{5 x}$ and $6 x \sqrt{5 x}$ .

$3 x \sqrt{6} + 2 x \sqrt{5 x}$