explain why you cant evaluate (-36)^0.5???

Question

for my h/w i got this question

Answer 1

(-36)^0.5 is the same as (36^0.5) * (-1^0.5)
(36^0.5) can be evaluated however there is no real value that is the square root of -1 and so that can't be evaluated.

To get around this the symbol i (or j) was defined as the square root of -1. On a number line this introduces a 2nd axis but this now represents imaginary numbers.

Answer 2

I assume that you only have the real numbers at your disposal at this point in time. The expression in your problem is the same as sqrt(-36). Since the square of a real number is either positive or zero, there is no value for the sqrt(-36). If you continue to take more math courses, then you will find that us mathematicians have found an answer to this problem.

Answer 3

Can you use imaginary numbers?

(-36)^(1/2) is the same as sqrt(-36)

Remember, two positives multiplied always equal a positive. Two negatives always equal a positive, so there are no real numbers whose square is a negative number.

To solve, you must use the concept of imaginary numbers, where i= the imaginary unit = sqrt(-1)

So the answer you must factor out the negative square root as so:

sqrt(-36) = sqrt(36)sqrt(-1)= sqrt(36)i = 6i

Hope this helps!

Answer 4

you can evaluate this unless you use imaginary numbers
^0.5 is another way of saying the square root of something, and since you're trying to find the square root of -36, this cant be so since you cannot root someting that is a negative number.

Answer 5

because you can't have a square root of a negative number - well not until you do higher level maths and then you use i or j