CBSE Class 10 Answered
1) let A be rational and B be irrational number prove that A+B is irrational number
2)prove that product of rational and irrational number is irrational number.
3)if a is rational and b is irratonal then a/b is irrational number.
Asked by | 11 Apr, 2011, 01:00: PM
Expert Answer
If a is rational and b is irrational, to prove that (a+b) is irrational.
We prove this result by contradiction,
let if possible (a+b) is rational.
Since (a+b) is rational and 'a' is rational and the difference of two rational number is rational,
so (a+b)–a is also a rational number.
This gives 'b' is rational.
Which contradict that "b" is irrational.
Hence our supposition is wrong and (a+b) is irrational.
Similar proof can be done for others.
Answered by | 11 Apr, 2011, 03:06: PM
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