how do you solve the square root of a negative number?

Question

its part of an equation like that one below and i dont how to solve do i just leave it like that

ex:

-9 plus or minus the square root of -9 divided by 3

Answer 1

The square root of a negative number is not a real number, it's an imaginary number. You would solve it the same why you would a real number, but the answer will be imaginary represented by i.

Therefore root of -1 would be imaginary 1.

Root of -16 would be imaginary 4.

Answer 2

remember the imaginary number i squared equals -1 so you can change it to -9 plus or minus the square root of 9i^2 divided by 3. so you should have -9 plus or minus 3i over 3.

Answer 3

The square root of a negative number cannot be any number in the real number system (that is, the real number line). This is because a number has to be negative, zero, or positive, so when multiplied by itself you either get zero (if the original number was zero) or a positive number back (because two positive numbers multiplied together will give you a positive, as will two negative numbers multiplied together). There is, however, the concept of "imaginary numbers". In this case, you let the variable "i" represent √-1. So √-81 = √-1√81 = 9i. A number like "9i" doesn't have any meaning related to numbers as we generally know them (real numbers). But the concept of imaginary numbers has a number of uses in mathematics, and strangely enough the real world too.

Answer 4

The square root of -1 is "i", the notation for an imaginary number. It simply does not exist in the set of real numbers.

If your question goes:

[-9 ± (sq. rt. -9)]/3

It becomes

(-9 ± 3i)/3

Because -9 = 9 * (-1). The square root of 9 is 3, and the square root of -1 is i. It ends up as 3i.

And, dividing properly, we end up with

-3 ± i

Answer 5

Unless you are studying imaginary numbers in your class or are expected to use them, you should not have a negative square root.
If you are, though, your example should be:
(-9(+,-)(-9)^.5)/3
(-9(+,-)3i)/3

i represents the square root of -1. But, your example looks like it's from a quadratic equation in which case you should probably try to rework your algebra.

Answer 6

its known as "imaginary" you cant get anything like it. IMPOSSIBLE but there is something you can do with it but i forgot. If anything i would put

(the square root of -9 / 3) +/- (-9). I think the answer is -10 or 8.

Answer 7

the letter i equals the square root of -1. so you the square root of -9 is equal to the square root of 9 times the square root of -1. other than that there is no answer to that question. you must use the imaginary number i.

Answer 8

square root of -1 is defined to be +/i

-9+/-sqrt(-9)/3 = -9 +/-3i/3 or -9+/-i that is 9+i and 9-i

Answer 9

The same way as if it were positive, except that you attach the symbol "i" to indicate that the result is imaginary.

Answer 10

(-9 ± √(-9))/3
(-9 ± i√9)/3
(-9 ±i3)/3
-3 ± i

HTH

Doug