Square Root Negative 1

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The numbers written inside the square root radical can be either ‘0’ or any positive integer in order to get a real solution as the ‘y’ value. If a negative number is written inside the square root, then the output becomes an imaginary number, commonly represented by ‘i’. Square root of -1, which can also be written as ‘√-1’ is called as the imaginary number and it is not considered a real number. √-1 is equal to ‘i’ which means the value of i = √-1.

Example 1: What is the simplified form of √-12?

√-12 is an imaginary number since it consists the negative sign inside the radical.

√-12 can also be written as: √(-1 * 12).

This is equal to √-1 * √12 and here √-1 is the ‘i’ value and is the imaginary number.

Hence we get: √-12 = i * √12 and now we can simplify √12.

This implies: √-12 = i * √(2* 2* 3) = i * 2√3.

Therefore the simplified form of √-12 = 2i√3.
 
Example 2: What is the simplified form of √-18?

√-18 is an imaginary number since it consists the negative sign inside the radical.

√-18 can also be written as: √(-1 * 18).

This is equal to √-1 * √18 and here √-1 is the ‘i’ value and is the imaginary number.

Hence we get: √-18 = i * √18 and now we can simplify √18.

This implies: √-18 = i * √(2 * 3 * 3) = i * 3√2.

Therefore the simplified form of √-18 = 3i√2.
 

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