Question

prove that root 5 is irrational

Answer 1

let assume that root 5 is a rational number

so p/q = root 5

a , b are co primes so

a/b = root 5

squares on both sides

a2/b2 =5

a2= 5b2

so  5 divide a2

so 5 divide a also

5 is a factor of a

similarly

5 is also a factor of b

so root 5 is a rational number

but root 5 is a irrational

so our assumption is wrong

Answer 2

Answer:

Step-by-step explanation:

bonjour

let us assume , to the contrary that root 5 is rational

as we know a and b are co primes

b is not equal to 0

root 5 = a by b

suppose a and b have a common factor other than 1,then we can divide by the common factor , and assume that a ana b are co primes

b root 5 = a

squarrying both sides

we get 5b sqaure= a square

a 2 is divisible by 5

and a is divisible by 5

so a=5c for some integer c

we get 3b square = 25c square

b square= 25c square

b square is divisible by 5

b is divisible by 5

hence contradiction is wrong root 5 is irrational

hope helps