Prove the 3√7 is irrational
Let us first prove that √7 is an irrational number:
let √7 be rational, then it can be represented as
√7 = p/q - irreducible fraction, where p,q are natural numbers
then
Because is divisible by 7, then is also divisible by 7,
then p=7k, where k is a natural number.
We get
- so q is divisible by 7.
It turns out that p - is divisible by 7 and q - is divisible by 7, i.e. contradiction,
because p/q is an irreducible fraction. So there is no rational number that is equal to √7.
And accordingly there is no rational number that is equal to 3√7.
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