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

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

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Answer 1 · 2015-09-14T13:14:45

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

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 $i$ $i$ times the square root of the positive numbers, because $i^{2} = - 1$ $i^2=-1$ by definition, and for example you have
$\sqrt{- 25} = \sqrt{(- 1) \cdot 25} = \sqrt{- 1} \cdot \sqrt{25} = i \cdot 5 = 5 i$ $sqrt(-25)=sqrt((-1)*25)=sqrt(-1)*sqrt(25)=i*5=5i$ .

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

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

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

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