what is the square root of -16?

Answer 1

It's impossible to calculate square roots of negative numbers in the first grades :), u need to have the notion of complex to calculate so it will be +4j or -4j

Answer 2

Square Root Of 16

Answer 3

A simple definition would suffice.
Complex Numbers are numbers in the form x+iy, both x and y are real(or in polar or exponential form, which aren't really necessary here)
i here is the square root of -1. Why isn't this represented by a number? Consider the possible options for a number such that when it is multiplied by itself yields -1,
these would be -1 and 1 if we stay true to the real number system. But (-1).(-1) = 1 and 1.1=1 so neither yield -1. Therefore a symbol i (j in some texts) is used to denote this.
Now values in the form yi where y is real are called imaginary numbers.
So considering the square root of -16,
note that,
V(-16) = V[(-1).(16)] = V(-1) . V16 = V(-1) . 4 = 4i or -4i (both plus and minus just like square roots of real numbers.

Answer 4

The square root of any negative number is known as an imaginary number.

The word "imaginary" here doesn't mean "doe not exist". It was coined by a mathematician who called them such because they are "not real numbers" - in other words, they don't lie on the line of real numbers that stretches from -infinity to +infinity, with -2, -1, 0- 1, 2, 3 and all the other numbers you've heard of lying on it.

The solution to the square root of -4 actually has two solutions, equally valid. The number can either be +4 x i (i is the square root of -1) or -4 x i, or simply ±4i.

The solution to any square root of a negative number is worked out exactly the same way. The square root of -2 is ±√2i; the square root of -9 is ±3i, and so on.

Answer 5

-16 is equal to -1 x 4^2, so the square root of -16 is equal to 4 times the square root of -1. This number is given the value of i, the imaginary number. So, the answer to your question is 4i.

Answer 6

Square root to any negative number is undefined. There is no meaning.

You need to understand that square to a number is equal to the reverse process of square root of a number.
Eg. 5^2 = 25 and square root 25 = 5, -5

As you can see, -5 is also an answer.
Therefore, any number, be it positive or negative, when you square the number, the result will always be positive. However, you cannot square root a negative number as no numbers, when you square it, will ever give you a negative number.

Thus, square too -16 is undefined.

Answer 7

4

Answer 8

4

Answer 9

4i

Negative numbers cannot be square rooted directly, they have to be done in Complex numbers. Square Roort of -1 is represented by 'i' and we take that out of the equation and square root the number which is 16 whose square root is 4 thus 4i is the answer.
Basic middle school maths

Answer 10

4

Answer 11

4