Algebra Examples

$x^{2} \sqrt{180} - \sqrt{5 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $36$ out of $180$ .

$x^{2} \sqrt{36 (5)} - \sqrt{5 x^{4}}$

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Move $6$ to the left of $x^{2}$ .

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

Step 1.4

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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Step 1.4.1

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

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

Step 1.4.2

Reorder $5$ and ${(x^{2})}^{2}$ .

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

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

Step 1.5

Pull terms out from under the radical.

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

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

Step 2

Subtract $x^{2} \sqrt{5}$ from $6 x^{2} \sqrt{5}$ .

$5 x^{2} \sqrt{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$