Question

prove 3+√2is irrational​

Answer 1

Answer:Let us assume the contrary that 3+root2 is rational.

Therefore we find two integers a and b such that 3+root2=a/b, where a and b are co-prime and b is not equal to 0.

3+root2=a/b

Root2=a-3b/b

Since a-3b and b are integers.

Therefore they are rational

Therefore root2 is also a rational number as LHS=RHS.

But is given that root2 is irrational

(the question is incomplete who typed it)

Therefore we have reached a contradiction

Therefore our assumption is wrong

Therefore 3+root2 is an irrational number.

The question who typed it is incomplete please

please check the question

Step-by-step explanation:

Answer 2

Answer:

Let us assume that 3+√2 be a rational number

it can be written as in the form of p/q

now 3+√2 = p/q

√2= p-3q/q

since p/q is rational number therefore p-3q/qis also rational number , hence √2 is rational number

but it contradict the fact that√2 is irrational number

hence we conclude that 3+√2 is an irrational number.

hope it will help you