Square Root of Negative Number

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Square root of a number is written under the square root radical symbol ‘√’ and the numbers inside the square root should be greater than or equal to ‘0’ to get a real solution. But if a negative number is inside the square root, then the solution is known ias an imaginary solution and it is written in terms of ‘i’. Square root of -1 is equal to ‘i’ and it represented as i = √-1. Therefore square root of negative numbers gives imaginary solutions.

Example 1: What is the value of the expression, √(-4)?

√(-4i) can be split further in order to simplify the expression.

This implies that √(-4) = √4 * √-1

Here, √4 can be written as √4 = √(2 * 2) = 2

Therefore, √4 = 2 and this gives √-4 = √4 * √-1 ==> √-4 = 2 * √-1.

And √-1 is equal to ‘i’ ==>√-4 = 2 * √-1 = 2 * i

Hence the value of the expression, √(-4) = 2i
 
Example 2: What is the value of the expression, √-27?

√(-27) can be split further in order to simplify the expression.

This implies that √(-27) = √27 * √-1

Here, √27 can be written as √27 = √(3* 3 * 3) = 3√3.

Therefore, √27 = 3√3 and this gives √-27 = √27* √-1 ==> √-27 = 3√3* √-1.

And √-1 is equal to ‘i’ ==> √-27= 3√3 * √-1 = 3√3 * i

Hence the value of the expression, √(-27) = 3i√3.
 
 
 
 
 
 

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