Question

prove that root 5 is irrational

Answer 1

hey mate here is your answer

let us assume that
$\sqrt{5}$
is a rational number where it is of the form p/q where p and q both are co-prime integers where q is not equal to 0

therefore

root 5=a/b
on squaring both sides,

5=a raise to 2/b raise to 2
➡5braise to 2=a raise to 2

therefore 5 divides a square
so 5 divides a

taking a=5m

5b raise to 2=5m the whole square
5b raise to 2=25m square
b=5m

therefore 5 divides b square
so 5 divides b

both terms, a and b have common factor 5

therefore our assumption is wrong
root 5 is an irrational number

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Answer 2

I hope it will help you

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