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It depends on how advanced you are. At school level (unless specialising in pure mathematics) you will be told that the squares of both negative and positive numbers are positive. There are, therefore, no numbers that have a negative square and so the square root of negative number cannot exist.


Calculators, including those built into computers will confirm this by issuing an error message.


However, when you study advanced mathematics you learn about the complex field and discover that negative numbers do have square roots. they are linked to the imaginary square root of -1, which is denoted by i.


Thus for example, sqrt(-16) = sqrt(16)*i=4i

and sqrt(-10) = sqrt(10)*i etc.


In a way, this is like being told in infant school that you cannot take 5 away from 2. Later on, you learn that you can and the answer is a new kind of number: a negative number!

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Q: What happens when I square root a negative number?
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Related questions

How do you do a square root of a negative number that is not a perfect square?

The square root of a negative number is not real.


Why is it impossible to square a negative number?

you can square a negative number but you can not square root a negative number


What is the square root of a negative number plus the square root of a negative number?

Nothing. You cannot have a square root of a negative number. The square root of negative one is called i, but i is an imaginary number. It does not exist and does not follow the properties of real numbers. (For example, if a and b are positive, then the square root of a times the square root of b is the square root of ab. But the square root of -7 is not the square root of 7 times i.)


How do you find the negative square root of 5?

A negative square root is an imaginary number.


How do you get the square root of negative 144?

square root of a negative number is imaginary square root of negative 1 is defined as i square root of negative 144 is sqrt ((144)(-1)) = 12i


Is the square root of negative 11 a real number?

No. In general, the square root of a negative number is an imaginary number, which is not a real number.


What is a negative square root defined as?

If you're referring to the square root of a negative number, it's an imaginary number.


Is negative the square root of 36 a whole number?

Negative the square root of 36 is -6, which is a whole number.


What is the square root of a negative number written in the form bi where b is a real number and you is the square root of the negative?

Imaginary number


The square root of a negative value is called an or complex number?

The square root of a negative value is called an imaginary number.


Is the square root of negative 16 a transcendental number?

No it is an Imaginary Number√-16 = 4ii is the square root of negative one


What is the number i?

i is the symbol for an imaginary number, a complex number with the property i2=-1. The square root of a negative number is the square root times i. For example, the square root of -9 = 3i.