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If 'a' is a positive rational number and 'n' is a positive integer greater 1. Prove that a n is a rational number.

If 'a' is a positive rational number and 'n' is a positive integer greater 1. Prove that an is a rational number.

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago

Hello student,
Please find the answer to your question below
Given a is a rational number
so it can be expressed as p/q where p,q are some integers and q>0
as n>1 and is a positive integer if n=2 then
a2=(p/q)2=(p*p)/(q*q)=rational (since product of two rational numbers is rational and also p/q is rational) similarly for n=3,4,......N by the principle of mathematical induction anis rational for all n>1 and n=postive integer

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