Given:
√3 + √4
To prove:
√3 + √4 is irrational.
Proof:
Let assume that √3 + √4 is rational
Therefore it can be expressed in the form of \(\frac{p}{q}\), where p and q are integers and q ≠ 0
√3 + √4 = \(\frac{p}{q}\)
\(\frac{p^2-q^2}{2pq}\) is a rational number as p and q are integers.
This contradicts the fact that √3 is irrational, so our assumption is incorrect.
Therefore √3 + √4 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.
