Question

given that root2 is irrational number.prove that(5+3root2) is an irrational number

Answer 1

hope this help.........

Answer 2

!!! Hi friends !!!

let 5+3√2 be rational

5+3√2 = a / b [where a and b are co prime nos]
          
3√2 = a / b - 5

3√2 = a- 5b / b

√2 = a- 5b / 3b

∴ a- 5b / 3b is rational 

∴ √2 is also rational

but it is given that √2 is irrational

this contradiction has arisen because of our wrong assumption that 5 + 3√2 is rational

∴ 5 + 3√2 is irrational

     Hence proved.......... ;D

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Hope this helps.................. :D