how do you square root a negative number?

Answer 1

There comes the concept of complex numbers!

If you dont want to deal with them, you can justify yourself that
square root of a negative number is NOT a real number, such that you can say its absurd.

However if you do want to describe them:

√-1 = i
which is a fundamental concept rather a definition.

Now, square root a negative number can be expressed as:
√(negative number)
=√(-1*positive number)

Lets consider an example.....say square root of -4
= √(-4)
= √(-1*4)
= i*2
= 2i

Properties of i or √-1
i² = -1
i³ = i²*i = -i
i^4 = i²*i² = -1*-1 = 1

Answer 2

You introduce i as the sqrt(-1) and multiply it by the square root of the absolute value of the number. Note that you have two roots, one negative and one positive times i.

sqrt(-9) = 3i and -3i, as an example.

If the concept of imaginary numbers is not part of your background (say in a course you are taking), just write such an answer as 3*sqrt(-1), with -1 still inside the radical as you would do with any irrational number.

Answer 3

Pretend it's a positive number, and then add the letter "i" to the square root to indicate it's the square root of a negative.

Answer 4

A negative number can be expressed as the positive number multiplied by -1. thus -9 will be 9 X -1.

So, the square root of - 9 can be written as sqrt (9 X -1) and we know that square root of two numbers a.b is sqrt.a multiplied by sqrt.b.

So, we can write, sqrt. (9 X -1) = sqrt. 9 X sqrt. -1

= 3 X sqrt. -1

Now, there is a special symbol for sqrt. -1 and that is i to denote its imaginary nature. So, we write

sqrt. - 9 = 3i

Answer 5

We use a complex number to describe the square root of a negative number. a complex number is usually written as X+iY

And i^2=-1
So, √-1=i, √-4=i2

Answer 6

you can't without using the imaginary number i which many other people have already explained. and unless you are in gr 11 math you ignore that anyways.

there is no answer to a question asking for a square root of a negative number. so write no answer

Answer 7

The same way you square root a positive number. You will just have a negative answer.

Answer 8

Very carefully. The concept of i = sqrt(-1) was developed many years ago to handle this problem. So the square root of -4 would be 2i.

Answer 9

i is an imaginary number defined as i² = - 1
Consider the following examples:-
√(- 16) = √(i² 16) = 4 i
√(- 32) = √(i² x 16 x 2) = 4√2 i
Hope these help.

Answer 10

In general we can write any number interms complex number such as z= a+ib, where a and b are reals and sqrt(-1)=i.
square root of z=square root(r)*(cos(theta+2k*pi)/2)+isin(theta+2k*pi)/2), k=0,1.

r= square root(a^2+b^2),
theta=tan^-1(b/a),