prove that root 2 + root 3 is a irrational number?
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HI !
Lets assume that 2 + √5 is rational.
Let ,
2 + √5 = r , where "r" is rational
√5 = r - 2
Here ,
RHS is purely rational, where as on the other hand , RHS is irrational.
This is a contradiction.
Hence our assumption [ that 2 + √5 is rational ] is wrong.
∴ 2 + √5 is irrational
Lets assume that 2 + √5 is rational.
Let ,
2 + √5 = r , where "r" is rational
√5 = r - 2
Here ,
RHS is purely rational, where as on the other hand , RHS is irrational.
This is a contradiction.
Hence our assumption [ that 2 + √5 is rational ] is wrong.
∴ 2 + √5 is irrational
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