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if a is a rational number and n is positive integer greater than 1 .prove that a^n is rational

if a is a rational number and n is positive integer greater than 1 .prove that a^n is rational

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question
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 thena2=(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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