Question

Show that 3 + root2 is an irrational number.

Answer 1

3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. But this contradicts the fact that √2 is irrational.. So, it concludes that 3+√2 is irrational..

Answer 2

Answer:

Let us consider that 3 root 2 is a rational. It can be written in the form p/q(p and q are co - primes)

p/q = 3 root 2

p/3q = root2

Now,

p/3q = integer / integer = rational number

But this contradicts the fact that root 2 is an Irrational number.

There fore, our assumption that 3 root 2 is a rational number is wrong.

Hence, 3 root 2 is an Irrational number

Step-by-step explanation:

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