Q. 114.1( 16 Votes )
Given: Any prime positive integer p.
To find: is an irrational number.
Concept used: Assume p to be rational number and prove it is irrational by contradiction.
Let assume that √p is rational
Therefore, it can be expressed in the form of , where a and b are integers and b≠0
Therefore, we can write
a2 = pb2
Since a2is divided by b2, therefore a is divisible by b.
Let a = kc
Here also b is divided by c, therefore b2 is divisible by c2. This contradicts that a and b are co-primes. Hence is an irrational number.
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