Question

prove √5is irrational pls mates explain.........​

Answer 1

let us take that root 5 is rational

root 5=a/b ; b is not equal to 0, a and b are co-primes when we cross multiple root 5=a/b we get

$\sqrt{5} b = a$

sqauring both sides we get

5b square =a square

a square is divisible by 5

a is also divisible by 5

then,

a= 5c

squaring both sides we get

a square = 5c square

putting the value of a square we get

5b square = 25c square

b square =5c square

b square is divisible by 5 and

b square is also divisible by 5.

hence a and b are divisible by 5 so they

are not co primes

this contradicts the assumption that root 5 is irrational.

Hence root 5 is irratinal

Answer 2

Answer:

let us take that root 5 is rational

a= 5c

a= 5csquaring both sides we get

a= 5csquaring both sides we geta square = 5c square

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c square

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c square

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 and

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 andb square is also divisible by 5.

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 andb square is also divisible by 5.hence a and b are divisible by 5 so they

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 andb square is also divisible by 5.hence a and b are divisible by 5 so theyare not co primes

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 andb square is also divisible by 5.hence a and b are divisible by 5 so theyare not co primesthis contradicts the assumption that root 5 is irrational.

a= 5csquaring both sides we geta square = 5c squareputting the value of a square we get5b square = 25c squareb square =5c squareb square is divisible by 5 andb square is also divisible by 5.hence a and b are divisible by 5 so theyare not co primesthis contradicts the assumption that root 5 is irrational.Hence root 5 is irrational.