Question

imaginary numberssimplify √-24

Answer 1

Answer:

$\sqrt[]{-24}=2i\sqrt[]{6}$

Explanation:

The square roots of negative numbers do not exist on the real line. They are called imaginary numbers. In these numbers there is a definition that help deal with cases with square roots of negative numbers.

$\sqrt[]{-1}=i$

With the above, it is easier to denote answers to the square root of negative numbers.

Given:

$\sqrt[]{-24}=\sqrt[]{-1\times24}$

We can write this as

$\begin{gathered} \sqrt[]{-1}\times\sqrt[]{4\times6} \\ \\ =\sqrt[]{-1}\times\sqrt[]{4}\times\sqrt[]{6} \\ \\ =i\times2\times\sqrt[]{6} \\ \\ =2i\sqrt[]{6} \end{gathered}$