Question

What is the $ \sqrt { - 25} $ ?

Answer 1

Hint: We are now going to be introduced to the concept of complex numbers , we know from experience that no square can be negative it can be either zero or a positive number, but what will happen if we have to find out the square root of a negative number , since squares are always positive finding root of negative numbers does not make sense . To accommodate for this anomaly mathematicians gave complex numbers,
The basis of these numbers help us find the square roots of negative number,
The complex number are based on one symbol $ i $ called as iota and
 $ {i^2} = - 1 $
These help in finding out the square root of negative numbers.

Complete step by step solution:
The complex numbers are based on square root of negative numbers The given question asks
 $ \sqrt { - 25} $ since the square root of negative numbers do not exist we have to write them as one symbol $ i $ called as iota and
 $ {i^2} = - 1 $
These help in finding out the square root of negative numbers.
So the number $ \sqrt { - 25} $
Can be said to be equal to
 $ 25i $ .
Hence the number $ \sqrt { - 25} $ will be $ 25i $
So, the correct answer is “$ 25i $”.

Note: Complex numbers unlike real numbers have two parts one part is the real part this part is the part of numbers we always solve or know which are in the set of real numbers, but the imaginary part on the other hand is the second part of the complex number which has a term called $ i $ or iota .The formula for a complex number is written below,
 $ Z = R + iC $
 $ R $ is the real part and $ C $ is the complex part.