Video Transcript
Find the value of the cube root of
0.027.
In order to answer this question,
we will consider two methods. In the first one, we will begin by
converting the decimal into a fraction. Using our knowledge of place value,
we know that 0.027 is the same as twenty-seven thousandths. This means that we are trying to
calculate the cube root of twenty-seven thousandths. Next, we recall that if 𝑎 and 𝑏
are integers and 𝑏 is nonzero, then the cube root of 𝑎 over 𝑏 is equal to the
cube root of 𝑎 over the cube root of 𝑏. We can therefore calculate the cube
root of 27 and the cube root of 1000 separately. Since three cubed is equal to 27,
the cube root of 27 is three. Likewise, as 10 cubed is 1000, the
cube root of 1000 is 10. The cube root of 27 divided by the
cube root of 1000 is therefore equal to three over 10 or three-tenths. And this is the value of the cube
root of 0.027. Writing this answer in decimal
form, we have 0.3.
We will now consider a second
method we could use to solve this problem. We begin by writing 0.027 as 27
multiplied by 0.001. As already mentioned, 27 is equal
to three cubed. In the same way, 0.001 is equal to
0.1 cubed. We can therefore rewrite the
original expression as shown. Using the fact that the cube root
of 𝑎 cubed 𝑏 cubed is equal to 𝑎𝑏, we can rewrite the right-hand side of our
equation as three multiplied by 0.1, which once again gives us a final answer of
0.3.
