2007-02-05 02:00:30 · 34 answers · asked by Roger U 1 in Science & Mathematics ➔ Mathematics
3i
There is no real number that you can multiply by itself to equal a negative, so you have to use the imaginary number "i" where i is such a number.
2007-02-05 02:17:44 · answer #1 · answered by C D 3 · 2⤊ 0⤋
To answer this question it helps to have a basic understanding of negative numbers.
As you are probably aware if you multiply any two negative numbers you always get a positive. For example:
-3 x -3 = +9. This could also be written as minus 3 squared.
If you want to reverse the square (ie take a root) you simply find the root of 9 which equals 3.
Although we have reversed the maths our answer is now positive. This is because all roots equal a positive number. This is shown on the y=x^2 graph. (http://vlado.fmf.uni-lj.si/sola/1996/campelj/kvadrf.jpg )
This is why the number i was invented - To show the square of a negative number. It is represented as the letter i because it is an imaginary number.
Therefore the squareroot of:
-1 = i
-4 = 2i
-9 = 3i
-16 = 4i
and so on.
I hope this helps.
2007-02-05 08:55:00 · answer #2 · answered by Chris W 1 · 0⤊ 0⤋
Square Root of -9 is +3i and -3i
where
i = sqrt(-1) - an imaginary number to denote the square root of negative numbers.
To Validate the solution
Square of +3i = (+3i) * (+3i) = ((+3) * (+3)) * sqr(i) = (9) * (-1) = (-9)
Square of -3i = (-3i) * (-3i) = ((-3) * (-3)) * sqr(i) = (9) * (-1) = (-9)
2007-02-08 07:27:12 · answer #3 · answered by Thorian 1 · 0⤊ 0⤋
There is no such thing as a (real)square root of a negative number. This is going into very advanced mathematical subject called Complex numbers where the sqrt(-1) = i (or in some books, esp Engineering j). Having stated this fact, since the sqrt(-1) is i, the sqrt of (-4) =2i, therefore, you should now be able to work out the sqrt(-9).
For your reference it is 3i.
2007-02-05 02:26:35 · answer #4 · answered by mr_maths_man 3 · 0⤊ 0⤋
You cant square root negative numbers.
Think about it -3 x -3 will yield +9
hence you will never be able to square root negative numbers within Real Numbers
If this question is in regards to complex numbers then the answer is just 3i
2007-02-05 02:08:17 · answer #5 · answered by Renesis 2 · 2⤊ 1⤋
You have to use what is known as Complex Numbers in a problem such as this.
In Complex Numbers i² = -1.
The number -9 may then be written as 9 i²
and the roots are:-
√(-9) = √( 9i² ) = 3i,- 3i
2007-02-05 02:12:41 · answer #6 · answered by Como 7 · 1⤊ 0⤋
The roots are 3i and -3i. Either of these squared is 9i² = -9.
2007-02-05 02:06:25 · answer #7 · answered by Anonymous · 3⤊ 0⤋
The answer is 3i
where i is an imaginary number equal to the square root of -1. The is no solution within the real numbers (no number multiplied by itself can give -1) so imaginary ones where created
2007-02-05 02:05:04 · answer #8 · answered by telleron 2 · 3⤊ 0⤋
Its equal to (9)^.5 times[ ( -1)^.5 which is an imaginary number designated as 'i".]
(9 x -1)^.5= 3 i
3 is a real quantity.
The imaginary number represent a real quantity reflected in the opposite direction.
2007-02-05 02:20:57 · answer #9 · answered by goring 6 · 0⤊ 0⤋
3i, where i is defined as the square root of -1. It's an imaginary number used in polar co-ordinates and trigonometry.
2007-02-05 02:10:06 · answer #10 · answered by igorolman 3 · 1⤊ 0⤋
3 i
2007-02-05 02:04:18 · answer #11 · answered by boobookittie 2 · 1⤊ 2⤋