Question

Prove that 3+root2 is an irrational number.

Answer 1

to prove that 3+root2 is an irrational number
lets take the opposite i.e 3+root2 is a rational number
hence 3+root2 can be written in the form a/b
hence 3+root2 = a/b
          root2 = 1/3 x a/b
          root2 = a/3b

here a/3b is rational and root2 is irrational
as irrational cannot be equal to rational 
3+root2 is irrational

hoped it helped you

Answer 2

prove :
Let 3+√2 is an rational number.. such that
3+√2 = a/b ,where a and b are integers and b is not equal to zero ..
therefore,
3 + √2 = a/b
√2 = a/b -3
√2 = (3b-a) /b
therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers..
It means that √2 is rational....
But this contradicts the fact that √2 is irrational..

So, it concludes that 3+√2 is irrational..
hence proved..

l hope it helped u..
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