Question

Prove that 2+√3 is irrational

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Answer 1

Step-by-step explanation:

Since, a, b are integers, (a2 + b2)/2ab is a rational number. √3 is a rational number. It contradicts to our assumption that √3 is irrational. Thus √2 + √3 is irrational.

Answer 2

Answer:

hope this helpful for you

Step-by-step explanation:

Let 2 + root 3 is rational number

therefore, 2 + root 3 = p/q , where p and q are co - prime

2 + root 3 = p / q

root 3 = p / q -2

root 3 = p -2q /q

here p, -2q and q are integers

p - 2q / q is rational

but root 3 is irrational

therefore LHS not equals to RHS

hence 2 + root 3 is irrational number