# What is the conjugate of 3 minus square root of 2?

Sep 29, 2015

It is $3 + \sqrt{2}$

#### Explanation:

By definition the conjugate of
$\textcolor{w h i t e}{\text{XXX}} \left(a + b\right)$ is $\left(a - b\right)$
and
$\textcolor{w h i t e}{\text{XXX}} \left(a - b\right)$ is $\left(a + b\right)$
The term "conjugate" only applies to the sum or difference of two terms.

"3 minus the square root of 2"
means (in algebraic form)
$3 - \sqrt{2}$

Applying the earlier definition with $a = 3$ and $b = \sqrt{2}$
we have
The conjugate of $\left(3 - \sqrt{2}\right)$ is $\left(3 + \sqrt{2}\right)$