how to simplify these square roots

Question

√-36

√-49

√-12

Answer 1

I'm assuming you are working with imaginary numbers.

 

You can never have a negative under the square root so we can factor out an i in each term to have the following:

 

i√36, i√49, i√12

 

Now we can take the square root of the first two terms quite easily. They simply become 6i and 7i.

 

The last one we must break down the 12 inside the square root. We can break that down into √(4)(3) which becomes 2√3.

 

So we are left with 6i, 7i, and 2i√3.

 

I hope that helped!

Answer 2

Negative square roots deals with imaginary numbers. A √-1 = i (look up imaginary units)

 

1. √-36 = √-1 * √36 which equals 6i

2. √-49 = √-1 * √49 which equals 7i

3. √-12 = √-1 * √12 (√12 breaks down into √4 * √3) which equals 2i√3