Simplify square root of 4x^2-1

$\sqrt{4 x^{2} - 1}$

Step 1

Simplify with factoring out.

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

$\sqrt{{(2 x)}^{2} - 1}$

Rewrite $1$ as $1^{2}$ .

$\sqrt{{(2 x)}^{2} - 1^{2}}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 1$ .

$\sqrt{(2 x + 1) (2 x - 1)}$