Question

proof √5 is an irrational number. and plz dm me or msg me in brainly i want to ask more​

Answer 1

HELLO

HERE IS UR ANSWER,

prove that √5 is irrational .

solution :-

late us assume that √5 is a rational number hence we can write √ 5 in the form of a/b where A and B are co-prime and no other factor than 1 .

Hence, √5= a/b

=> squaring both the side ,

root 5 whole square = a divided by b whole square

=> 5= a^2/ b ^2

=> 5b^2 = a^2

=> a^2 /5 = b^2

thus, is divided by a^2

so 5 divided with a also .. { eq -1 }

a/5 = c, where c the is a integer.

=> a= 5c

=> 5b^2 = (5c)^2

=> 5b^2 = 25c^2

=> b^2 = 5 c^2

=> b^2/5 = c^2

Hence , 5 divided with b square also ..(eq-2)

5 divide with both A and B. so, A and B have a factor of 3 there for a and b and not coprime . hence our assumption is wrong.

by contradiction,

√5 is an irrational number .

HOPE IT HELP U