# How do you simplify 2/sqrt(-24)?

May 27, 2016

$\frac{- \sqrt{6} i}{6}$

#### Explanation:

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

When you have an irrational number in the denominator, the simplification is done by multiplying both numerator and denominator by the conjugated complex of the denominator:

$\frac{2}{\sqrt{24} i} = \frac{2 \left(- \sqrt{24} i\right)}{\sqrt{24} i \left(- \sqrt{24} i\right)} = \frac{- 2 \sqrt{24} i}{24}$

Now, simplify the fractions, by replacing 24 by its prime decomposition:

$\frac{- 2 \sqrt{24} i}{24} = \frac{- 2 \sqrt{{2}^{3} \times 3} i}{{2}^{3} \times 3} = \frac{- {2}^{2} \sqrt{2 \times 3} i}{{2}^{3} \times 3} = \frac{- \sqrt{6} i}{6}$