State where( underoot 6+underoot 9) is rational or irrational

1.	State where( underoot 6+underoot 9) is rational or irrational
Answer» Let root 6 + root 9 V rational root 9 equal to 3 root 6 + 3 equal to P by Q suppose P and Q have a common factor other than one root 6 + 3 equal to a upon B where A and B are co primes root 6 equal to a upon B + 3 root 6 equal to a + 3 B upon B since A and B are integers we get a + 3 B upon B is rational root 6 is rational but this contradict fact that root 6 is irrational this contradiction arise because of incorrect assumption that root 6 + root 3 is irrational hence root 6 + 3 is irrational

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