CBSE Class 10 Answered

image quality is very poor, managed to read first question. Too many number of questions should not be asked in one posting.

Hence only first question is answered.

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First question :-

Prove that  is irrational  where x and y are prime .

Answer :-

Let is rational number so that

  ........................... (1)

where p and q are integers .

By squaring eqn.(1) , we get

Hence we get

where a and b are integers .

Hence if we assume that is rational number , then we get   is a rational number .

But x and y are prime numbers and squareroot of product of prime numbers is not a rational number .

Hence the initial assumption , ' is rational number ' is not correct.

Hence  is irrational number .