Or I'll just put a negitave sign here

And so we can re write this expression right over here

1 to the third power is equal to 1 time 1 times 1, which is equal to 1

And so our answer to this

(Laughter)

So negative 512 thats the same thing, so let me re write the expression this is the same thing as the cube root of negative 1 times 512.

Or 2 to the 9th power is 512

Square Root

Square root

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.

Which is the same thing as the cube root, which is the same thing as the cube root of 1 times the cube root of 512 and this one is pretty straight forward to answer.

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

Square Root Scale

For example you cannot do this.

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

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.

So it becomes 1 times, times this business right here

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

So the square root is this big check looking thing.

Well we go up three and down three.

Insert square root

5 minus 1 is 4.

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.

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

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.

So they just want to keep it general.

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.

Great cubicuboctahedron

We have a split wing.

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?