Square Root

Square root

We learned in the imaginary numbers video, that hopefully you've watched, that every now and then in certain equations you end up with a square root of a negative number.

So x is equal to 2 is 4.

You could rename it with anything really, is equal to the square root of x minus 1.

Square Root Scale

Let me show you how this works on an example.

By definition, a square root is something A square root of 9 is a number that, if you square it, equals 9.

We can solve the mystery simply by looking at the actual difference between these two values.

For example you cannot do this.

Add them together, and then take the square root, or the principal root.

So the square root is this big check looking thing.

Well we go up three and down three.

And then you get y is equal to and I'm doing this on purpose the plus or minus square root, because it can be the plus or minus square root.

Plus or minus the square root of 4 9 is 2 3, right?

So that's a negative number.

In our case, the correct range for x is 0 to maxint.

Insert square root

5 minus 1 is 4.

Well, it's when you have a negative number under here.

Is equal to the determinant of your matrix squared.

And I'm just going to re write it as y to the 1 2 power.

And this is just multiplying a binomial.

So let's see where that gets me.

And the same idea actually, can be done with any function.

So 4x plus 1 I'm just taking the square root of both sides.

Of x minus 1.

And then if we go to 2, let's see, 2 minus 1 is 1.

There's no real solution.

When we're taking the square root, it's not just the positive square root.

Now that said we can do it if only one of them are negative or both of them are positive on this thing.

I'll skip the actual computation of square roots here because this is the subject of another class, but before we return to the actual square root, we want to make sure that the square root actually is a square root.

Because then you could say, oh well the square root of negative nine is the same thing as i times the square root of nine, which equals threei.

Which tells us that the focal length is equal to the square root of this.

You can always every perfect square has a positive or a negative root.

When you just see a number under a radical sign like this, this means the principal square root of 9.

So we're going to take the positive square root, or just the principal root, which is just the square root sign, of both sides.

1,344 plus 25.

1,369 over 16.

OK, so it's minus 5 plus or minus 37.

When x is equal to 9, what's y?

So we're shifting it over to the right by 5.

The square root of x.

So this point is equivalent to that point.

That's just the numerator.