What is the square root of -81????

Question

isnt that like nnot possible? my friends say theres an answer other than (NO SOLUTION) but my calculator says DOMAIN ERROR
plus i dont even think its gonna work.
Email me at [e-mail]
Please tell me
oh yeah email me a graph of this Problem and ill definitly pick yur answer as best answer on any of your future answers to my questions!!!!! Y= -3*(x squared)+4x-1

it has to be a parabola, and if yu dont know what that is then dont answer.

Answer 1

Your calculator only works with REAL numbers.

To extend the number system so that NEGATIVE numbers could have a square root (plus lots of very real and practical consequences!), the symbol 'i' was introduced, satisfying the basic defining equation:

i^2 + 1 = 0, or i^2 = -1, so i = sqrt(-1).

In those terms, the square root of (-81) is +/- 9 i.

To confirm this, (+/- 9 i)^2 = + 81 (i^2) = - 81.

You can't "graph" this on the real plane, as you understand that.

However, ways of representing complex numbers of the form
z = x + iy WERE developed, and help greatly in visualizing and understanding what's going on.

This may all seem very mysterious to you now, but I hope you get to learn about it.

A historical analogy: there was a time when humanity only knew about POSITIVE numbers! It required the invention of 0 (zero) and the concept that there were "other numbers," on the "other side of zero," to give us those very strange beasts (to people at the time), NEGATIVE NUMBERS.

As to your SECOND problem (and please, SEPARATE different problems, or the words "this Problem" are ambiguous): This is a parabola, open downwards. You REALLY ought to work out some sets of (x, y) values for yourself, but I'll give you two additional useful points --- one literally;

The VERTEX of this parabola is at (x, y) = (2/3, + 7/3), or (2/3, + 2.3333..). What's more, the parabola is symmetric about the vertical line x = 2/3. That means that if you "flip" the parabola over, using that line as an axis of either reflection or rotation, you get the same parabola again; that may help you to make a more accurate graph.

Live long and prosper.

Answer 2

-3x^2 + 4x - 1 = 0

x = -4 + sqr(16 - 4(-3)(-1))/2(-3)
x = -4 - sqr(16 - 4(-3)(-1))/2(-3)

2(-3) = -6

-4(-3) = 12(-1) = -12

x = -4 + sqr(16 - 12)/-6
x = -4 - sqr(16 - 12)/-6

16 - 12 = 4 sqr(4) = 2/-6 = -1/3 or -0.33333
-4 + (-0.333333) = -4.33333
-4 - (-0.3333) = -3.6666

x = -4.33333
x = -3.66666

You can get the square root of a negative number but it requires an advance calculator like the TI 86. sqr(-81) should be 9i i standing for imaginary number. Wish I had a TI86 but their over 100 bucks right now.

where did you get -81 its not part of the equation you gave, but you are right it is a parabola very skinny one at that.

Answer 3

The answer is that there is no answer. There is a solution, but it is not a real number , it is imaginary.

Your friend is somewhat wrong.

The square root of a negative number is called imaginary, represented by the simple i , which has a value of -1.

The answer would be the Square Root of 81i , so if you pull out the i and then change it to represent -1, you get -1(Sq. Rt) of 81 which is back where you started.

The answer is not a real number. It is imaginary.

Answer 4

when you do a square root of a negative number you use the "imaginary number" rule, so that the "i" unit replaces the negative under the square root (radical) and you do the square root of 81, which is 9, and add an "i" to the end of it: 9i. I think that's the answer, i'm not sure what math you're in, but this is from the basics.

Answer 5

TI calcs aren't smart enough to do that, regretfully, explaining why it gave you an error (but interestingly then can multiply with it...). Remember that you can convert the negative square root of 1 into the imaginary number "i", then just do the square root normally. So Think of Sqrt(-81) as Sqrt(81)i, which as 50 people already said, is 9i and -9i.

Answer 6

In the realm of real numbers, the square root of -81 does not exist. Most calculators are only capable of taking in real numbers and solving for real number solutions.

However, the square root of 81 has a solution, in the realm of complex numbers. In such a realm, there exists a number, i, which is defined to be the square root of -1.

sqrt(-81) = sqrt( (-1) * (81) ) = sqrt(-1) * sqrt(81) = i * 9 = 9i

So the (positive) square root of -81 is 9i.

Answer 7

9 x 6 = 54. D, B, and C are the answer. Square root of 2916 is 54. Hah, I am the only one that gave all the possible answers, I should win the 10 pts. :)

Answer 8

The question here should be WHAT DOES SQUARE ROOT OF -81 HAVE TO DO WITH THIS PROBLEM?

You have an upside down parabola here, that intersects x at 1/3 and 1, and intersects y at -1.

Answer 9

Yeah, it only works if the negative sign is outside the square root sign.
x=-3, y=-40
x=-2, y= -21
x=-1, y= -8
x=0, y=-1
x=1, y=0
x=2, y=-5
x=3, y=-16

if you graph that, it will be a parabola

Answer 10

you can take out the negative and replace it with (i) and you can break down the 8 into (2-2-2) so you end up with:


2i x 2^(1/2)

which reads as two i times the square root of two