Question

Give that under root 2 is irrational, prove that (5+3 under root 2 ) is an irrational number.
Fast plz

Answer 1

5+3ROOT 2 IS IRRSTIONAL
5+3ROOT 2 = a/b
3root2=a/b-5
3root2=a-5b/b
root2 =a-5b/3b
root2 is irrational but a-5b/3b is rational...

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