Square roots of negative numbers?

Question

help me with this question

what is the square root of negative 6

Answer 1

i*sqrt(6) for complex numbers (no solution for real numbers)

Answer 2

Hi nick-

To take the square root of a negative number, mathematicians designated 'i' to be √-1. Numbers including an 'i' are called "imaginary". Using this, we can use the rule that √a ·√b = √ab to find √-6.

We can say that √-6 is equal to √-1 · √6, and so √-6= i√6. A general rule for finding √-a is that it is equal to i√a.

Hope this helped!

Answer 3

the answer is i times square root of 6. it's a complex number because i stands for the square root of negative numbers.

Answer 4

it's an imaginary number. You can't have a rational square root of a negative, since if you multiply two negs you get a positive, and two positives also yields a positive, and to be a root, they need to be equal. If you had an imaginary "half negative" or something like that, you might be able to have one.

Answer 5

By definition, i^2 = -1 => i = +/- sqrt -1 (keep positive value only)
=> i = sqrt -1

then sqrt -6 = sqrt (-1 x 6) = sqrt -1 x sqrt 6 = i x sqrt 6 =i x 2.45

Answer : 2.45i


An other example: sqrt -64 ?

sqrt -64 = sqrt (64 x -1) = sqrt 64 x sqrt -1 = 8 X i = 8i


In general : sqrt -a = sqrt(a x -1) =sqrt a x sqrt -1 = sqrt a x i

= i sqrt a

Answer 6

in real number, it is not possible to square root a negative number. However, you can do in in complex number.

sqr(-16)= 4i and -4i

Answer 7

The answer is an imaginary number
i(6)
the squareroot is in parentheses