Question

Show that $3+ {\sqrt{2}}$ is an irrational number

Answer 1

SOLUTION :  

Let us assume , to the contrary ,that 3 +√2 is rational. Then,it will be of the form a/b where a, b are co primes integers and b ≠0.

3 + √2 = a/b

√2 =  a/b - 3

since, a & b is an integer so, a/b - 3   is a rational number.  

∴ √2 is rational  

But this contradicts the fact that √2 is an irrational number .

Hence, 3 +√2 is an irrational .

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Answer 2

heyya there here is ur answer
hope it helps