Precalculus Examples

$\sqrt{125 x^{3}} - \sqrt{5 x}$

Step 1

Rewrite $125 x^{3}$ as ${(5 x)}^{2} \cdot (5 x)$ .

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Step 1.1

Factor $25$ out of $125$ .

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

Step 1.2

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

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

Step 1.3

Factor out $x^{2}$ .

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

Step 1.4

Move $5$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$5 x \sqrt{5 x} - \sqrt{5 x}$