Algebra Examples

$3 x \sqrt{180 x^{5}} - 10 \sqrt{180 x^{7}}$

Step 1

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

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Step 1.1

Factor $36$ out of $180$ .

$3 x \sqrt{36 (5) x^{5}} - 10 \sqrt{180 x^{7}}$

Step 1.2

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

$3 x \sqrt{6^{2} \cdot 5 x^{5}} - 10 \sqrt{180 x^{7}}$

Step 1.3

Factor out $x^{4}$ .

$3 x \sqrt{6^{2} \cdot 5 (x^{4} x)} - 10 \sqrt{180 x^{7}}$

Step 1.4

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

$3 x \sqrt{6^{2} \cdot 5 ({(x^{2})}^{2} x)} - 10 \sqrt{180 x^{7}}$

Step 1.5

Move $5$ .

$3 x \sqrt{6^{2} {(x^{2})}^{2} \cdot 5 x} - 10 \sqrt{180 x^{7}}$

Step 1.6

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

$3 x \sqrt{{(6 x^{2})}^{2} \cdot 5 x} - 10 \sqrt{180 x^{7}}$

Step 1.7

Add parentheses.

$3 x \sqrt{{(6 x^{2})}^{2} \cdot (5 x)} - 10 \sqrt{180 x^{7}}$

Step 2

Pull terms out from under the radical.

$3 x (| 6 x^{2} | \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 3

Remove non-negative terms from the absolute value.

$3 x (6 x^{2} \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 4

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 4.1

Move $x^{2}$ .

$3 (x^{2} x) (6 \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 4.2

Multiply $x^{2}$ by $x$ .

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Step 4.2.1

Raise $x$ to the power of $1$ .

$3 (x^{2} x^{1}) (6 \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{2 + 1} (6 \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 4.3

Add $2$ and $1$ .

$3 x^{3} (6 \sqrt{5 x}) - 10 \sqrt{180 x^{7}}$

Step 5

Multiply $6$ by $3$ .

$18 x^{3} \sqrt{5 x} - 10 \sqrt{180 x^{7}}$

Step 6

Rewrite $180 x^{7}$ as ${(6 x^{3})}^{2} \cdot (5 x)$ .

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Step 6.1

Factor $36$ out of $180$ .

$18 x^{3} \sqrt{5 x} - 10 \sqrt{36 (5) x^{7}}$

Step 6.2

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

$18 x^{3} \sqrt{5 x} - 10 \sqrt{6^{2} \cdot 5 x^{7}}$

Step 6.3

Factor out $x^{6}$ .

$18 x^{3} \sqrt{5 x} - 10 \sqrt{6^{2} \cdot 5 (x^{6} x)}$

Step 6.4

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

$18 x^{3} \sqrt{5 x} - 10 \sqrt{6^{2} \cdot 5 ({(x^{3})}^{2} x)}$

Step 6.5

Move $5$ .

$18 x^{3} \sqrt{5 x} - 10 \sqrt{6^{2} {(x^{3})}^{2} \cdot 5 x}$

Step 6.6

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

$18 x^{3} \sqrt{5 x} - 10 \sqrt{{(6 x^{3})}^{2} \cdot 5 x}$

Step 6.7

Add parentheses.

$18 x^{3} \sqrt{5 x} - 10 \sqrt{{(6 x^{3})}^{2} \cdot (5 x)}$

Step 7

Pull terms out from under the radical.

$18 x^{3} \sqrt{5 x} - 10 (| 6 x^{3} | \sqrt{5 x})$

Step 8

Remove non-negative terms from the absolute value.

$18 x^{3} \sqrt{5 x} - 10 (6 | x^{3} | \sqrt{5 x})$

Step 9

Multiply $6$ by $- 10$ .

$18 x^{3} \sqrt{5 x} - 60 | x^{3} | \sqrt{5 x}$