Given: 2 - 3√5
To prove:
2 - 3√5 is irrational.
Proof:
Let assume that 2 - 3√5 is rational
Therefore it can be expressed in the form of \(\frac{p}{q}\), where p and q are integers and q ≠ 0
Therefore we can write
\(\frac{2p-q}{3q}\)is a rational number as p and q are integers.
This contradicts the fact that √5 is irrational, so our assumption is incorrect.
Therefore 2 - 3√5 is irrational.
Note:
Sometimes when something needs to be proved, prove it by contradiction.
Where you are asked to prove that a number is irrational prove it by assuming that it is rational number and then contradict it.
