Question

Find the square root of -625 and select from the given options. Use\[\sqrt{-1}=i\].
A) 5
B) -5
C) 25i
D) -25i

Answer 1

Hint: To start to solve this question always remember that \[\sqrt{-1}=i\] and then proceed to use the negative of 625 so as to calculate the square root of the given number. We have the square root of a negative number is not defined until \[\sqrt{-1}=i\] is given.

Complete step-by-step answer:
We have to calculate the square root of -625. To do so we use the fact that \[\sqrt{-1}=i\].
Because the given number in the question has a negative sign therefore, it cannot be solved without using \[\sqrt{-1}=i\].
Now, we proceed to use the square root of negative of 625 so as to calculate the square root of the given number, which gives,
\[\begin{align}
  & \sqrt{-625}=\sqrt{-(25)(25)} \\
 & \Rightarrow \sqrt{-625}=\sqrt{(-1)(25)(25)} \\
\end{align}\]
Using the fact given in the question as \[\sqrt{-1}=i\] we get,
\[\begin{align}
  & \sqrt{-625}=\sqrt{(-1)(25)(25)} \\
 & \Rightarrow \sqrt{-625}=i\sqrt{(25)(25)} \\
 & \Rightarrow \sqrt{-625}=i25 \\
 & \Rightarrow \sqrt{-625}=25i \\
\end{align}\]
Therefore, we get the value of the square root of -625 as 25i.
Analyzing the options, we get that the correct option from the given ones is 25i that is option (c).

Note: The possibility of error in this question can be taking minus one out of the root and also substituting \[\sqrt{-1}=i\] at the same time which will get the answer as -25i, which is wrong because if we are taking root of -1 as I then it will not come out as minus one.