Algebra Examples

$- \sqrt{150 x^{5}} + x \sqrt{6 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $150 x^{5}$ as ${(5 x^{2})}^{2} \cdot (6 x)$ .

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Step 1.1.1

Factor $25$ out of $150$ .

$- \sqrt{25 (6) x^{5}} + x \sqrt{6 x^{3}}$

Step 1.1.2

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

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

Step 1.1.3

Factor out $x^{4}$ .

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

Step 1.1.4

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 1.1.5

Move $6$ .

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

Step 1.1.6

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

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

Step 1.1.7

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $5$ by $- 1$ .

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

Step 1.4

Rewrite $6 x^{3}$ as $x^{2} \cdot (6 x)$ .

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Step 1.4.1

Factor out $x^{2}$ .

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

Step 1.4.2

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

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

Step 1.4.3

Add parentheses.

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $x$ by $x$ by adding the exponents.

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Step 1.6.1

Move $x$ .

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

Step 1.6.2

Multiply $x$ by $x$ .

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

Step 2

Add $- 5 x^{2} \sqrt{6 x}$ and $x^{2} \sqrt{6 x}$ .

$- 4 x^{2} \sqrt{6 x}$