So in my calculator I'm going to type in 196.5 and we'll raise it to, now remember to have these parentheses here, otherwise your calculator will just raise it to the first and then divide everything by 3. So here you're going to raise it to the one third power. Because a fractional root, or excuse me a fractional expone is actually taking a root. So we take the cube root of both sides and I'm going to say that the cube root of our cube is r, and in my calculator, what I'm going to type, if your teacher hasn't shown you, the way you type this in is you're going to type in 196.5 and then to tell it to raise it to a fraction. Now that the only thing that we have here is an r cubed, we can take the cube root and isolate r. So now I'm going to get another decimal, I'm going to divide this by pi and I get 196.5 we'll round. I can't take the cube root just yet so what I'm going to do is I'm going to divide both sides by pi. So what we've done is we've isolated pi times r cubed. I'm going to type that into my calculator. So I'm going to multiply both sides by three fourths. To isolate r here, first we're going to take the reciprocal of four thirds. The last one that we're going to look at is something that you'll be solving when you're talking about the volume of the sphere. The negative is not going to be one of your answers. So notice that with the cube root you're only going to end up with this one answer. If we go back to this cube root however, if I said x could be -3, let's just look at this real briefly. Because, 2 times the square root of 5 times itself is 20 and if I took the negative of that multiplied by itself we'd end up with 20 as well. Since we're in Geometry and we're almost always talking about distances, we're going to almost always take the positive root. Now if we go back to our first problem, something that we'll notice is that I could have said that this was positive or negative 2 times the square root of 5. I have to do the same operation on the other side and the cube root of 27 is going to be 3. So the cube root of x cubed is going to be x. Well to undo cubing something, I'm going to take not the square root but the cube root. So we are going to say that r is equal to 2 times the square root of 5. And I can say that 20 is 10 times 2, but I don't know either of those square roots as a whole number but I can write it out as square root of 4 times square root of 5. So the square root of 20 the way I like to simplify that is to think of it as two square roots being multiplied together. So to solve this for r, I need to undo squaring which is squaring square rooting. On the left side here we have pi divided by pi which is 1, and we have 80 divided by 4, which is 20. The only thing left on the right side is r squared. So it should look familiar, it's something that you did last year in Algebra. So I'm going to divide both sides by 4 pi. First step is you're going to eliminate what's multiplying r squared and that is 4 pi. So you're going to have to do a couple of steps here. The first one you have an equation with one variable r and r is being squared. In Geometry you're going to solve with square roots and with cube roots.
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