Q. 84.8( 8 Votes )

Prove that <span

Answer :

5√2 is an irrational number and subtraction of a rational number and an irrational number is an irrational number.

, 4 - 5√2 is irrational, where 5√2 is an irrational number while 4 is a rational number.


Alternative - Assume that 4 - 52 is rational
4 - 52 = a/b , where a and b are integers .
- 52 = a/b - 4
5√2 = 4 - a/b
5√2 = 4b/b - a/b
2 = (4b – a) / 5b
we know that a, b, 4 and 5 are integers and they are also rational {i.e RHS is rational}
therefore2 will be rational.
but we know that2 is irrational.
there is a contradiction
so, 4 - 52 is an irrational number


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