7.1 From Division to Roots
In the previous chapter, we calculated with square roots. Did you know that there are also “third roots of” and “fourth roots of” and so forth?
Here is an example:
Written: ?
Read as: "fifth root of 32"
We can ask the question: *which number multiplied by itself five times becomes 32*? If we factories it into its primes 32 looks as follow (if you forgotten how to factorise a number into its primes, see page 4.2)
32 = 2 **·** 2 **·** 2 **·** 2 **·** 2 =
2^{5}
The answer becomes that: 2^{5/5 }= 2.
Did you know that calculating with roots can be described as repetitive division?
Here we divide 32 by 2 five times:
1:st time |
32 ÷ 2 = 16 |
2:nd time |
16 ÷ 2= 8 |
3:rd time |
8 ÷ 2 = 4 |
4:th time |
4 ÷ 2 = 2 |
5:th time |
2 ÷ 2 = 1 |
So 32 divided by 2 five times is equal to 1. |