Question

show that 3 + root 2 is irrational number

Answer 1

the value of root 2 is 1.414 reapting decimal 1.414+3=4.414 and it is reapting decimal so it is irrational number

Answer 2

3+√2 is irrational number 
assume that 3+√2 is a rational number 
  3+√2=a/b
√2=a/b-3
squaring on both sides
√2²=(a/b-3)²
2=(a/b)²-2(a/b)(3)+3²
2=a/b²-6a/b+9
2=a/b²+3a/b
2=a²+3ab
   --------------
        b²
=a²+3ab
--------------
     2b²
hence our assume is wrong 
it is an irrational number