Question

Simplify the square root of -121.
A) –11i
B) 11i
C) –11
D) 11

Answer 1

What is \(\sqrt{-1} \) ?

Answer 2

I have no Idea I thought you couldn't square root a negative number.

Answer 3

Using real numbers, you are correct. The square root of a negative number has no meaning.

Answer 4

So then why did it give me options to choose from?

Answer 5

The answer has to be one of these.
A) –11i
B) 11i
C) –11
D) 11

Answer 6

Let's go back to basics.
The square root is the opposite operation of the square, the exponent 2.

For example, \(5^2 = 25\).
The opposite operation is the square root.
\(\sqrt{25} = 5\)

Answer 7

So then, \[\sqrt{-121}=11 ?\]

Answer 8

Since a positive number times a positive number = positive
And also a negative number times a negative number = positive,
there is no numner you can multiply by itself and get a negative number.

Answer 9

Since square root is the opposite of squaring, for real numbers, there does not exist a square root of a negative number.

Answer 10

What does A and B mean then?

Answer 11

That is why mathematicians invented imaginary numbers.
The invention of imaginary numbers allows you to take the square root of a negative number.

Answer 12

The basic idea with imaginary numbers is this definition:

\(\sqrt{-1} = i\)

Answer 13

So then it would be A) -11i

Answer 14

Since squaring is the opposite operation of square root, then it follows that is

\(\sqrt{-1} = i\), then \(i^2 = -1\)

Answer 15

No, but we're almost there.

Answer 16

Then B? 11i

Answer 17

Keep in mind this basic idea of imaginary numbers:

\(\sqrt{-1} = i\)

Answer 18

Then it's B) 11i

Answer 19

Now we deal with your problem.

\(\sqrt{-121} = \sqrt{121 \times (-1)} = \sqrt{121} \times \sqrt{-1} = 11 \times i = 11i \)

Answer 20

You are correct. It is choice B.
The important thing is that you understand why it is 11i.
I showed it to you step by step above.

Answer 21

Thank you :) can you help me with a few more problems?

Answer 22

Examples using \(\sqrt{-1} = i\)

\(\sqrt{-4} = \sqrt{4} \times \sqrt{-1} = 2i\)

\(-\sqrt{-144} = -\sqrt{144 \times (-1)} = -\sqrt{144}\times \sqrt{-1} = -12i\)

Answer 23

You're welcome, and yes.

Answer 24

It's number 2 I'm entirely lost.

Answer 25

Please make a new post for each new question.

Answer 26

Okay, one second.