Precalculus Examples

$\sqrt{x^{2} - 25}$

Step 1

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

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\sqrt{(x + 5) (x - 5)}$