Why cant you find the square root of a negative number?

Question

I really need to know why. Please give full answer.

Answer 1

The FULL answer to your question is in four stages.

1) Why can't you find a number that added to 4 gives 1? Answer: you can, it's -3, which is a NEGATIVE number. If all you have are positive numbers, then you can't.

2) Why can't you find a number that multiplied by 5 gives 3? Answer, you can, it's 3/5, which is a FRACTIONAL number. If all you have are whole numbers, then you can't.

3) Why can't you find a number that's the square root of 2? Answer: you can, it's sqrt(2) or 1.41421356..., which is a REAL number. If all you have are whole numbers and fractions, then you can't.

4) why can't you find a number that's the square root of -4? Answer: you can, it's 2i, which is an IMAGINARY number. If all you have are real numbers, then you can't.

Except for engineers and mathematicians, nearly everybody is completely happy with stages 1, 2 and 3, and totally boggled by stage 4. But for engineers and mathematicians, stage 4 is just an obvious and natural next stage. The good news for the rest of us is that there is no stage 5.

Answer 2

The square root of a number (n) is a number that you can multiply by itself to get a product equal to n.
If you're trying various possible values, looking for the square root of -4 (as an example), you'll find that:
1. If you try a positive value and multiply it by itself, the product is positive. Obviously, the square root of -4 can't be positive.
2. If you try a negative value and multiply it by itself, the product is again positive. So, obviously the square root of -4 can't be negative.
3. What else is there, besides positive and negative? Zero? Again, it's obvious that 0 times 0 is 0, which is not -4.

So we've tried every possible category of REAL numbers (positive, negative, and zero), and none can conceivably be the square root of -4.

Solution: Create a different type of number that we call "imaginary." Define the number i (i for imaginary) as the square root of -1. Then the square root of -4 is 2 i.
The other square root of -4 (all numbers have two square roots) is -2 i.

Admittedly, negative numbers are an odd concept, but they often serve a useful purpose in solving mathematical problems and sometimes scientific or engineering problems.

Answer 3

Well in theory you can by calling Root -1 = i or known as an imaginary number. The reason why Root -1 is undefined is because a when you square a positive or negative number it never ends up negative. For example Root(-4), there is no non imaginary number that when you square it you can get -4 because when you square any number it becomes positive. however if you take in concideration of imaginary number it would be 2i.

Answer 4

You can't find the square root of a negative number because a square root is two identical numbers that can be multiplied together to get the original number. Only a positive and a negative can be multiplied together to give you a negative number.

Answer 5

lets say negative 4 for example. if you times by -2 by -2 it is going to equal 4(two negatives make a positive) and if you times 2 by 2 it's still 4 so thats why you cant find a square root of a negative number

Answer 6

The square root of a number x is a number such that when you multiply it times itself you get x.
The square root of 25 is either 5 or -5 because
5 times 5 = 25 = -5 times -5
When you multiply two positive numbers you always get a positive number. When you multiply two negative numbers you always get a positive number.
the only way to get a negative number (through multiplication) is by multiplying a positive times a negative.
Now you can see why you don't get a real number when you take the square root of a negative number.

Answer 7

let the square root of -1 = a

there for -1 = a^2

but we know that a^2 is always positive. so it's i irrational for it to equals a negative number.

thats why u can't square root a negative number.

hope i helped. Good Luck !!!

Answer 8

It is possible to find the square root of a negative number I hope this website can explain it better than I can.

http://mathforum.org/library/drmath/view/52613.html

It's not possible for a calculator to tell you the answer because the majority are not programmed to be able to do so.

Answer 9

If you square a negative number it becomes positive.

Answer 10

In the real number system, any number--positive or negarive--multiplied by itself is a positive number. Therefore, no number squared can be negative.