Question

Prove that √3 is an irrational number Hence show that 2 √3 -8 is also an irrational number​

Answer 1

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