Question

prove that ( √2 + √7) is an irrational number​

Answer 1

Suppose (sqrt(2) + sqrt(7)) is not irrational but rational number and equal to r. Then ,

sqrt(2) + sqrt(7) = r ==> sqrt(2) = r - sqrt(7) ==> 2 = r^(2 ) + 7 - 2r sqrt(7) or

sqrt(7) = (r^(2) + 5)/2r . But r.h.s. here is a rational number while l.h.s. is an irrational number, a contradiction .

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