Question

Imaginary numberssimplify √-24

Answer 1

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

Step-by-step 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*24}`

We can write this as

`\begin{gathered} \sqrt[]{-1}*\sqrt[]{4*6} \\ \\ =\sqrt[]{-1}*\sqrt[]{4}*\sqrt[]{6} \\ \\ =i*2*\sqrt[]{6} \\ \\ =2i\sqrt[]{6} \end{gathered}`