We can take out one x and we're still left with one x on the inside but we know that this has to be positive because we can't take a negative out of the square root so once again we have to put in absolute value signs okay because wherever comes out of the square root has to be positive. What happens is we are squaring it so that will become positive and then taking the square root of it so it's actually going to stay positive because we don't know if x is positive or negative, we have to put absolute value signs from the outside to make that term positive okay, so square root of x cubed. The problem is is that we don't know if x is positive or negative right? Say x was negative 3, just like we had over here. Okay, so let's go over here the square root of x squared okay that is made up of 2 x's so we know that we can simplify this as an x. Okay when we have a even root all of our answers have to be positive okay? So these are numeric representations but now we're going to variables. Negative 2 times itself 3 times is negative eight so what we have looked at here is when we have a odd root okay cube root here we can have a positive answer or a negative answer. Okay, cube root of 8 has three 2's in eight so this comes out to be 2 and the cube root of negative 8 is -2. When we square a negative number, we actually get a positive so -3 times -3 is 9 square root of 9 is again 3. 3 squared is 9, square root of nine is 3. Okay next, square root of -4, we need 2 numbers that will give us -4 that's not going to happen okay this is a not a real number okay later on we'll actually talk about how we can do this but we're not there yet okay? So square root of 3 squared. Okay so it's starting off, square root of 4, easy example we know the square root of 4 is 2 because 2 times 2 is equal to 4. The absolute value and square roots, so what we're going to do now is talk about absolute values and sometimes what happens is we actually need an absolute value when we give our answer and so what we're going to do is look at a number of examples and talk about when we need them and when we don't.
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