Foundation
Mathematics Foundation
Properties of Real Number
Irrational Number
Rational Numbers
Question
is an ......... number.
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Solution
(a and b are co-prime i.e. they have no common factors)....... (1)
5b2= a2 (squaring both sides)
Therefore 5 divides a2
As per Fundamental Theorem of Arithmetic, 5 divides a.
Let's take it as a = 5c,
5b2 = 25c2
b2 = 5c2
As per Fundamental Theorem of Arithmetic, 5 divides a.
So a and b have 5 as a common factor but a and b have only 1 common factor 1 from equation (1) so it is not rational.
So, we conclude that is irrational.
Therefore, D is the correct answer.
5b2= a2 (squaring both sides)
Therefore 5 divides a2
As per Fundamental Theorem of Arithmetic, 5 divides a.
Let's take it as a = 5c,
5b2 = 25c2
b2 = 5c2
As per Fundamental Theorem of Arithmetic, 5 divides a.
So a and b have 5 as a common factor but a and b have only 1 common factor 1 from equation (1) so it is not rational.
So, we conclude that is irrational.
Therefore, D is the correct answer.