PROVE THAT √13 is irrational Hence, show that 5+ 3√13 is irrational - Maths - Real Numbers

Question

PROVE THAT √13 is irrational Hence, show that 5+ 3√13
is irrational

Ankita Agarwal · Accepted Answer

Dear Student ,
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Let us assume the contrary   i
e; 5+313 is rational  ∴ 5+313= ab , where ‘a’ and ‘b’ are coprime integers and b ≠ 0313= ab – 5 313= a−5bb Or 13 = a−5b3b  Because ‘a’ and ‘b’ are integers a−5b3b  is rational That contradicts the fact that 13 is irrational
 The contradiction is because of the incorrect assumption that (5 + 313) is rational
  So, 5 + 313 is irrational

Regards

PROVE THAT √13 is irrational. Hence, show that 5+ 3√13 is irrational.