Express the cube root of 256 minus the cube root of four in its simplest form.
So when simplifying, we need to look at the cube root of 256 because the cube root of four doesn’t actually reduce. So 256, is it divisible by a number that’s a perfect cube? It is; 64 is a perfect cube and 64 times four is 256. So using the property that we can take the cube root of 𝑎 times 𝑏 and replace it with the cube root of 𝑎 times the cube root of 𝑏, so we can do that here.
So now that we’ve separated it, the cube root of 64, we know that four cubed is the same thing as 64 and if you cube root something cubed, the cube and the cube root will disappear. So that’s actually equal to four. Now let’s go ahead and bring down everything else. So we have four times the cube root of four minus the cube root of four. So they have the cube root of four in common and there is a one out front of the cube root four and there’s a four of- out front of that cube root. So we can combine the four and the negative one. So we have four minus one and then we keep the cube root of four. It’s almost the same as thinking of the cube root of four as an 𝑥, four 𝑥 minus one 𝑥 is equal to three 𝑥 cause we took four minus one. Therefore, four minus one is three.
So our final answer would be three cube root four.