Prove that root5 is an irrational

1.	Prove that root5 is an irrational
Answer» Let root5 is rational no. rational no. are p/q, qnot equal to 0 , p&q are co prime number √5=p/q√5q=p Squaring on both side(√5q)square=psquare5qsquare Let, us consider as root 5 is rational,where pandq are co primes √5=p÷q then √5q=p where q divides p ,so in our assumtion the root 5 is rational ia wrong ,so in the contradiction root 5is rational is correct Let us assume that √5 is a rational number.we know that the rational numbers are in the form of p/q form where p,q are intezers.so, √5 = p/q p = √5qwe know that \'p\' is a rational number. so √5 q must be rational since it equals to pbut it doesnt occurs with √5 since its not an intezertherefore, p = √5qthis contradicts the fact that √5 is an irrational numberhence our assumption is wrong and √5 is an irrational number.

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