Q. 103.9( 17 Votes )

Prove that (2 +√3

Answer :

√3 is an irrational number and addition of a rational number and an irrational number is an irrational number.


, 2 + √3 is irrational, where √3 is an irrational number while 2 is a rational number.


Alternative - Assume that 2 +3 is rational
, where a and b are integers.


we know that a, b and 2 are integers, therefor a - 2b is also an integer

therefore3 will be rational.
but we know that3 is irrational.
there is a contradiction
so, 2 +3 is an irrational number

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