Following the same steps from the other videos, first we're going to switch our x and our y. Once we have that grouping by itself, we then need to take a certain root to get rid of it. Before it was the square root, this time since it's cubed, we're going to take the cubed root of both sides. And then still solve for y. Now remember, cubed root does not have the plus or minus in front of it. So we get this final answer.
So with cubed roots, we don't have to worry about making sure that underneath here is positive because you actually can have a negative under a cubed root.
Let's look at fourth root. Same first step, switch the x and y. Now that the grouping it is by itself, we're going to take a certain root – we're going to take the fourth root. Now the fourth root does require plus or minus in front of it and then we solve for y, negative two plus or minus 4th root of x. Now the end of this one we have to make sure that x is positive because we have the fourth root. X is greater than or equal to zero and there's our condition. This is equal to negative 2 plus or minus the fourth root of x if x is greater than zero.
So how can you remember – I'm not going to go through each and every number for you – how can I remember which one requires this little condition here and which one doesn't? Well if you have an odd number – a third root, fifth root, seventh root, ninth root and so on and so forth, do not need the conditions. You don't need to set what is underneath the root greater than or equal to zero. If you have an even root, such as 2, 4, 6, 8, so on and so forth, you need the condition so you set whatever is underneath the root greater than or equal to zero to show that it's positive.
