Question

prove that√3 is an irrational number hence ,show that 7+2√3 is also an irrational number​

Answer 1

Step-by-step explanation:

If possible, let √3 be a rational number.

(i) ∴ a/b = √3 , where a and b are integers and co-primes Squaring both sides, we have From equation (I)

(ii), we have 3 is a factor of a and b which is contradicting the fact that a and b are co-primes. Thus, our assumption that √3 is rational number is wrong. Hence, √3 is an irrational number. (ii) Let us assume to contrary that 7 + 2√3 is a rational number. p – 7q and 2q both are integers, hence √3 is a rational number. But this contradicts the fact that √3 is irrational number. Hence 7 + 2√3 is an irrational number.

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