Algebra Examples

$\sqrt{72 x^{5}} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $72 x^{5}$ as ${(6 x^{2})}^{2} \cdot (2 x)$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$\sqrt{36 (2) x^{5}} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.2

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

$\sqrt{6^{2} \cdot 2 x^{5}} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.3

Factor out $x^{4}$ .

$\sqrt{6^{2} \cdot 2 (x^{4} x)} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.4

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

$\sqrt{6^{2} \cdot 2 ({(x^{2})}^{2} x)} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.5

Move $2$ .

$\sqrt{6^{2} {(x^{2})}^{2} \cdot 2 x} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.6

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

$\sqrt{{(6 x^{2})}^{2} \cdot 2 x} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.1.7

Add parentheses.

$\sqrt{{(6 x^{2})}^{2} \cdot (2 x)} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.2

Pull terms out from under the radical.

$| 6 x^{2} | \sqrt{2 x} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.3

Remove non-negative terms from the absolute value.

$6 x^{2} \sqrt{2 x} + 2 x^{2} \sqrt{18 x} - x \sqrt{2 x^{3}}$

Step 1.4

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

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Step 1.4.1

Factor $9$ out of $18$ .

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

Step 1.4.2

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

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

Step 1.4.3

Add parentheses.

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 1.7

Multiply $3$ by $2$ .

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

Step 1.8

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

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Step 1.8.1

Factor out $x^{2}$ .

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

Step 1.8.2

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

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

Step 1.8.3

Add parentheses.

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

Step 1.9

Pull terms out from under the radical.

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

Step 2

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

$12 x^{2} \sqrt{2 x} - x (| x | \sqrt{2 x})$

Step 3

Reorder factors in $12 x^{2} \sqrt{2 x} - x (| x | \sqrt{2 x})$ .

$12 x^{2} \sqrt{2 x} - x | x | \sqrt{2 x}$