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RD Chapter 1 Real Numbers Ex 1.5 Solutions

Question - 11 : - Prove that for any prime positive integer p, √p is an irrational number.

Answer - 11 : -

Suppose √p is not a rational number
Let √p be a rational number
and let √p = a/b
Where a and b are co-prime number
 
 
But it contradicts that a and b are co-primes
Hence our supposition is wrong
√p is an irrational

Question - 12 : - If p, q are prime positive integers, prove that √p + √q is an irrational number

Answer - 12 : -


Hence proved.

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