Solve 𝑥 cubed equals 27 over eight.
So if we take a look at this problem, the first step that we need to do solve it is to take the cube root of each side of the equation. And we do that, because the cube root is the inverse of cubed, and we can see that our 𝑥 term is 𝑥 cubed. So when we do that, we get 𝑥 is equal to the cube root of 27 over eight. So now what we can do is use a rule that we know. That rule is the cube root of 𝑎 over 𝑏 is equal to the cube root of 𝑎 over the cube root of 𝑏.
So, we can use this to rewrite our equation. So now we have 𝑥 is equal to the cube root of 27 divided by the cube root of eight. Well now what we can do is simplify. And we can do that because both 27 and eight are cube numbers. So we’re gonna get 𝑥 is equal to three over two. And we got that because the cube root of 27 is three because three multiplied by three multiplied by three is 27. And the cube root of eight is two because two multiplied by two multiplied by two is eight.
It’s worth noting here that we didn’t have to include any different answers. It’s a common mistake here might be to also include negative three over two. And the reason that we don’t include the negative answer is because a negative multiplied by negative is a positive, multiplied by another negative gives a result which is negative. So therefore, we’re trying to find root 27 not root negative 27. So therefore, that’s why we only have a positive answer. If we had an even root, so for instance the square root or the fourth root, then we can consider both negative and positive results.