How i prove irrational number type question. Irrational topic is very important topic of class 10th. What is the easiest way for solving this question of real number chapter exercise 1 .3 Prove that √5 is irrational

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Let us assume, that

√5 is rational number.i.e.

√5 = x/y (where, x and y are co-primes)y

√5= xSquaring both the sides, we get,

(y

√5)^{2}= x^{2}⇒5y

^{2}= x^{2}……………………………….. (1)Thus, x

^{2}is divisible by 5, so x is also divisible by 5.Let us say, x = 5k, for some value of k and substituting the value of x in equation (1), we get,

5y

^{2}= (5k)^{2}⇒y

^{2}= 5k^{2}is divisible by 5 it means y is divisible by 5.

Clearly, x and y are not co-primes. Thus, our assumption about

√5 is rational is incorrect.Hence,

√5 is an irrational number.