Solving an equation with a square root and a higher root power, so this problem we are looking at a cube root. The steps of solving an equation with a radical are always the same, we want to first get our root by itself take it side your appropriate power to get rid of the root, solve for our variable and then check.
Let’s go through that process right now. First thing we want to do is isolate our root. So we want to get this term cube root of x minus 1 by itself. In order to do that we first need to subtract 3 from both sides we end up with 4 cube root x minus 1 is equal to 8 and then I always like to get the coefficient away as well.
You could move on leaving it there but typically you are just going to get bigger numbers that’s going to make your life a little bit uglier so what we are going to do is divide by 4 to get that root completely by itself.
Our cube root x minus 1 is equal to 2 so now we have the root by itself we want to get rid of the root, we have a cube root so in order to get rid of this root we have to cube it. We cube one side we have to cube the other cube root of cubed just becomes the inside so this is x minus 1 to the third is 8 add 1 is leaves us with 9.
We always want to go back check to make sure our answer works plug in 9, 9 minus 1 is 8 cube root of 8 is 2 4 times 2 is 8 plus 3 is 11.
So this answer actually checks out so by going through the steps of solving a quadratic equation we are able to solve this problem.