Question

Show that √13 is irrational

Answer 1

hey hope it helps u
see attachment

Answer 2

hey mate !!!

let us assume on the contrary that√13 be a rational number .then , there exist positive integer a and b such that :-


let √13 be rational number.




=> √13=a/b


where a and b are co- prime :, their HCF is 1 .



now ,



√13= a/b .


on squaring both side



$13 = a ^{2} \div b ^{2}$



$13b ^{2} = a ^{2}$



$13 \div a ^{2}$





because :-
$13 \div 13b ^{2}$


13/a .





now, let => a = 13c



a= 13c



$a ^{2} = 169c ^{2}$


$13b ^{2} = 169c^{2}$


$b ^{2} = 13c ^{2}$



$b ^{2} = 13c ^{2}$




$13 \div b^{2}$


therefore


13/b .




now ,





we can observe that a and b have at least 13 as Common Factor but it contradict the fact that a and b are coprime.




this means that our assumption is not correct




hence ,


√13 is irrational number.




hope it helps!!!!!



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thanks