Question

Prove that (3 + root 2) is an irrational​

Answer 1

Answer:

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Step-by-step explanation:

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..

Answer 2

Answer:

for proving 3+ √2 as an irrational

first we have to,

assume 3 + √2 as a rational number

hence, 3 + √2 = p/ q ( were p and q are co- prime integers)

√2 = p/q -3 =( -3q - p)/q

so now here the RHS is an irrational number and the LHS is a rational number

therefore, this is a contradiction for our assumption

hence, it is proved that 3 + √2 is an irrational number