# How do you rationalize the denominator and simplify 1/(sqrt3-2)?

Sep 30, 2015

Multiply the numerator and denominator by bye conjugate of the denominator to get:
$\textcolor{w h i t e}{\text{XXX}} - \left(\sqrt{3} + 2\right)$

#### Explanation:

The conjugate of a two-term expression $\left(a + b\right)$ is $\left(a - b\right)$ and visa versa.
The product of conjugates $\left(a + b\right) \times \left(a - b\right)$ is ${a}^{2} - {b}^{2}$

For the given example, the conjugate of $\left(\sqrt{3} - 2\right)$ is $\left(\sqrt{3} + 2\right)$

$\frac{1}{\sqrt{3} - 2}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{\sqrt{3} - 2} \times \frac{\sqrt{3} + 2}{\sqrt{3} + 2}$

color(white)("XXX")=(sqrt(3)+2)/((sqrt(3)^2-2^2)

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt{3} + 2}{3 - 4}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt{3} + 2}{- 1}$

$\textcolor{w h i t e}{\text{XXX}} = - \left(\sqrt{3} + 2\right)$