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
Bharat Desikan , 11 Years ago
Grade 10
10 grade maths> if a is a rational number and n is positi...
1 AnswersSHAIK AASIF AHAMED
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
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
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on 10 grade maths
How do you find the Maclaurin series for tanx?
How do you find the Maclaurin series for tanx?
10 grade maths
1 Answer Available
Last Activity: 8 Months ago
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
10 grade maths
1 Answer Available
Last Activity: 8 Months ago
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
10 grade maths
1 Answer Available
Last Activity: 8 Months ago
Find the arithmetic mean of the first ten odd natural numbers.
Find the arithmetic mean of the first ten odd natural numbers.
10 grade maths
1 Answer Available
Last Activity: 8 Months ago