Cube root and reciprocal
Cube root
To find the cube root of a number, we have to find out which number when multiplied by itself twice gives that number. This is the same as trying to find out the length of the side of a cube when you know its volume.
For certain values we can achieve this without a calculator. However, more often or not, we will have to use one.
If we were asked to find the cube root of 1,728, we may see this written as \(\sqrt[3]{1728}\). Notice this is different to the square root symbol because there is a small subscript 3 in front of the \(\sqrt{}\). Using the cube root button on the calculator we see that \(\sqrt[3]{1728}\) = 12.
This means that if we had a cube with a volume of 1,728, its side lengths would be 12.
Reciprocal
The definition of reciprocal is often misunderstood. The reciprocal of a number is the number you would have to multiply it by to get the answer 1.
Look at the following reciprocals:
The reciprocal of 2 is \(\frac{1}{2}\)
The reciprocal of 3 is \(\frac{1}{3}\)
The reciprocal of 4 is \(\frac{1}{4}\)
The reciprocal of 5 is \(\frac{1}{5}\)
The reciprocal of 6 is \(\frac{1}{6}\)
You should have noticed the pattern that the reciprocal of a number is 1 over the number. Another interesting point is that the reciprocal of a reciprocal is the original number.
The reciprocal of \(\frac{1}{2}\) is 2.
The reciprocal of \(\frac{1}{3}\) is 3.
The reciprocal of \(\frac{1}{4}\) is 4.
The reciprocal of \(\frac{1}{5}\) is 5 and so on.
Question
What is the reciprocal of -1?
As we would have to multiply -1 by -1 to obtain the result 1.
-1 is its own reciprocal.
We could also answer this question by evaluating \(\frac{1}{-1}\) = -1.
