What is the Square Root of Negative 4? (-4)?

Question

If 2 x 2 = 4 then the square root of 4 is 2
If -2 x -2 = 4 then the square root of 4 is -2 Also!
So the square root of 4 is both 2 & -2

Considering that the above is true.

What is the Square Root of -4?

Answer 1

2i

Answer 2

What is the Square Root of Negative 4? (-4)?

2*2 = 4 (positive 4, no good)
-2*-2 = 4 (positive 4, no good)
2*-2 = -4 (negative 4, good).

So the √-4 = +2*-2. But can this be correct ? It depends on the definition of 'Square root'.

If you consider the square root to mean: Two numbers that are the same, when multiplied together, gives the required result. Then the about answer of +2 and -2 can't be right.

If you consider the square root to mean: Two numbers that are the same regardless of sign, when multiplied together, gives the required result. Then the about answer of +2 and -2 is correct.

If the about information is not excepted as an answer, then you will have to use complex numbers. ì = √(-1).

Answer 3

Answer: 2i.

To understand this, picture 2 number lines, at right angles to each other, intersecting at 0. The horizontal line is the line of Real numbers. The vertical line is the line of Imaginary numbers.

The lines follow strict rules. Choose any point on the Real line, other than 0... say, -2. If you multiply the chosen number by a positive real number like 3, you wind up 3 times further from 0, moving in the same direction: -6. If you multiply the -2 by another neg real number, like -3, you go to the same position you did before, -6, then reverse the sign... answer, 6. It reverses the direction traveled from 0 on the real line.

The imaginary number lines have different rules. If you multiply or divide by an imaginary number, then you should picture a 90 degree shift, from one line to another. 2i x 2i = -4 (90 degree shift counterclockwise); -2i x -2i = -4 (90 degree shift clockwise).

I hope this helps you visualize it. If not, try to find it in a book. It helped me a lot.

Answer 4

There is no such thing as a square root of -4. Because actually, the square root of any number is the Absolute Value.

The square root means you need two of the same number of the same sign. to obtain -4 you can only have it by multiplying 2 with -2, so there is no such thing as the square root of -4.

You could cheat by using imaginary numbers, "complex" numbers which manipulates the square root of -1, but your solution will not be in the "real" numbers.

Answer 5

You need to invent a new type of number, called an imaginary number. Call it "i". i^2 = -1, that's just the definition of it.

So the square root of -4 is simply 2i :)

Check : 2i * 2i = 4 * i * i = 4i^2 = 4(-1) = -4

P.S. Koopa : nope, i is totally different from -1. i is the square root of -1.

P.S. Kamaole : nice try, but no. Two negatives multiplied give you a positive.

Answer 6

Square Root of -4 is not possible but it is possible in imaginary numbers.

Square Root of -4 = Square Root of 4 x Square Root of -1
= 2 x i
= 2i

Note:
in imaginary number Square Root of -1 is i.

Answer 7

If you use the imaginary number i to represent the square root of -1, then there are *two* roots to -4.

Everyone seems to have forgotten, just like the example of 4 that there are two roots to -4.

You can check that 2i and -2i are the correct answers:

(2i)² = 2i x 2i = 2² x i² = 4 x -1 = -4
(-2i)² = -2i x -2i = (-2)² x i² = 4 x -1 = -4

So the answers are:
2i and -2i

Answer 8

The sqaure root of any number is by definition positive, i.e. given the number x, then we define the square root of x as follows:

sqrt(x) = |y| where y*y = x

To say 2i is the square root is not correct. 2i is not a real number. Square roots were defined for real numbers, not complex numbers. Complex numbers do not really exist even though we have created an entire mathematics topic out of them called complex analysis.

Answer 9

(-4)^(1/2)

= (4 * -1)^(1/2)

= 4^(1/2) * (-1)^(1/2)

= 2 * i

= 2i

"i" is an imaginary quantity equal to the square root of negative one.

Answer 10

its 2i because of since the square of 4 is 2 there you get your 2 but since the number is negative and a negative square cannot exist you need the imaginary number i.

Answer 11

the square root of any negative number is an IMAGINARY number.
meaning the numbe ris neither positive nor negative, like the number 0.
other than that everything is the same
so
x^2 = -4
x = i2
the i for imaginary