Question

which of the following is not irrational
(a) 1+root5
(b)1-root5
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Answer 1

Answer:

Let 1+root 5 be a rational no.

=> 1 + root 5 =p/q where p and q are integers and

q is not =0

=> root 5 = p -q/q

p-q/q is a rational no. this against the fact that root 5 is an irrational no. therfore our assumption is wrong hence 1+ root 5 is an irrational no.