Video Transcript
Find the cube root of two cubed.
In this question, we are asked to evaluate an expression involving the cube root of a cube. The easiest way to answer this question is to recall that taking the cube root and cubing are inverse operations. In general, we have that for any real number 𝑎, the cube root of 𝑎 cubed is equal to 𝑎. If we set 𝑎 equal to two, then we see that the cube root of two cubed is equal to two.
We could stop here. However, it is useful to see where this result comes from. To see this, we can start by recalling what we mean by the cube root of a number. If 𝑏 is any real number, then we say that the cube root of 𝑏 is the number whose cube is 𝑏. In other words, if the cube root of 𝑏 is equal to 𝑐, then we must have that 𝑐 cubed is equal to 𝑏. If we substitute 𝑏 is equal to two cubed into this definition, then we see that if the cube root of two cubed is equal to 𝑐, then we must have that 𝑐 cubed is equal to two cubed. The only real solution to the equation 𝑐 cubed equals two cubed is 𝑐 is equal to two. Hence, the cube root of two cubed is equal to two.
