To prove: is irrational.
Let assume that is rational
Therefore it can be expressed in the form of , where p and q are integers and q≠0
Therefore we can write,
Squaring both sides we get,
Apply the formula ( a - b )2 = a2 + b2 - 2ab in ,
is a rational number as p and q are integers.
This contradicts the fact that √3 is irrational, so our assumption is incorrect.
Therefore 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.
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