Prove that root 5 is an irrational number

Asked by admin @ 24/08/2021 in Math viewed by 348 People

Prove that root 5 is an irrational number.

Answered by admin @ 24/08/2021

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 = √5q
we know that 'p' is a rational number. so √5 q must be rational since it equals to p
but it doesnt occurs with √5 since its not an intezer
therefore, p =/= √5q
this contradicts the fact that √5 is an irrational number
hence our assumption is wrong and √5 is an irrational number.

hope it helped u :)

Prove that root 5 is an irrational number

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