Question

Simplify: -r-75 O A - Si OB. - Siva O c. 5i O D. - 5iv3

Answer 1

First we write the expression

`\begin{gathered} -\sqrt[]{-75} \\ \text{Simplifying, we have} \\ -\sqrt[]{-75}=-\sqrt[]{-1*3*25} \end{gathered}`

Therefore,

`-\sqrt[]{-75}=-\sqrt[]{-1}*\sqrt[]{3}\text{ }*\sqrt[]{25}`

Hence,

`-\sqrt[]{-75}=-\sqrt[]{-1}*\sqrt[]{3}\text{ }*5`

In mathematics, there is a symbol, i, used to define complex numbers.

i is as defined below

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

Therefore,

`\begin{gathered} -\sqrt[]{-75}=-i*\sqrt[]{3}\text{ }*5 \\ -\sqrt[]{-75}=-5i\sqrt[]{3} \end{gathered}`

Hence, the expression simplified is

-5i√3

D