# How do you simplify 2/(square root of -24)?

Sep 14, 2015

$\frac{2}{\sqrt{- 24}} = \frac{1}{\sqrt{6} i}$

#### Explanation:

Since the square root of a negative number doesn't exist among the real numbers, you'll have do deal it with complex numbers. In this set, the square root of a negative number equals $i$ times the square root of the positive numbers, because ${i}^{2} = - 1$ by definition, and for example you have
$\sqrt{- 25} = \sqrt{\left(- 1\right) \cdot 25} = \sqrt{- 1} \cdot \sqrt{25} = i \cdot 5 = 5 i$.

In your case, $\sqrt{- 24} = \sqrt{\left(- 1\right) \cdot 24} = \sqrt{- 1} \cdot \sqrt{4 \cdot 6} = \sqrt{- 1} \cdot \sqrt{4} \cdot \sqrt{6}$
which thus equals $2 \sqrt{6} i$.

So, $\frac{2}{\sqrt{- 24}} = \frac{2}{2 \sqrt{6} i} = \frac{1}{\sqrt{6} i}$, canceling the $2$'s