Question

show that 3+√2 is irrational number.​

Answer 1

Answer:

let is assume that 3+√2 is rational

let,3+√2=a/b(where a and b are co primes thus they have a common HCF=1)

ATQ,√2=a/b-3

we know that √2 is irrational

so, a/b-3 will also be irrational(because lf one side is irrational then another will also be irrational)

so, our supposition is wrong

3+√2 is irrational

Answer 2

Answer:

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..