Answer:
![\sqrt[]{-24}=2i\sqrt[]{6}](https://img.qammunity.org/2023/formulas/mathematics/college/bhmh4ag6ixk93szfz9nktdjd8ln67p2rwj.png)
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](https://img.qammunity.org/2023/formulas/mathematics/high-school/6auedmvsax8nlo4hpms2kngcv15a6lmlel.png)
With the above, it is easier to denote answers to the square root of negative numbers.
Given:
![\sqrt[]{-24}=\sqrt[]{-1*24}](https://img.qammunity.org/2023/formulas/mathematics/college/qzxb12k1niurzycc785jat97yeus2wicgq.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/ryqldsbcdb2e8s6abiwhdcio8dyvwt8dsl.png)