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Prove that √5 is irrational. Q.1

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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


1 Answer

  1. Let us assume, that 5 is rational number.

    i.e. 5 = x/y (where, x and y are co-primes)

    y5= x

    Squaring both the sides, we get,

    (y5)2 = x2

    ⇒5y2 = x2……………………………….. (1)

    Thus, x2 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,

    5y2 = (5k)2

    ⇒y2 = 5k2

    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.

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