Question

Prove that 3 + 2 √7 us an irrational.​

Answer 1

Answer:

let 3+ 2 √7 be rational number

             3 + 2 √7=p/q

             2√7=p/q-3

              2√7=p-3q/q

             √7=p-3q/2q

therefore, the LHS side is irrational ,and RHS side is rational

                 so both are not equal

therefore,   3 + 2 √7 is an irrational

Step-by-step explanation:

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Answer 2

Explanation:

Let us assume that 3+2√7 is rational

Then,

3+2√7=a/b where a and b are co primes

=> 2√7=a/b+3=(a+3b)/b

=> √7=(a+3b)/2b

We know that √7 is a irrational no and cannot be expressed i the form p/q, this proves the above statement wrong

The contradiction has arisen due to our wrong assumption that 3+2√7 is rational

=>3+2√7 is irrational