Question

prove that root 5 is irrational​

Answer 1

Answer:

Let we assume that root 5 is irrational no

now, then, root5=a/b

let ,a and b are co prime numbers having no common factor other than one.

now, squaring on both sides

(root5)2= (a/b)2

now, 5=(a/b)2

here , b2=a2/5

now,a2 is divisible by 5.

let, a=5c

now put this in b2=a2/5

so you get a and b both are divisible by 5

So,our assumption is wrong root 5 is irrational no

Answer 2

Answer:

let us assume root 5 is rational number

√5 = a/b a and b are co prime

√5b =a

squaring both side

5b^2 = a^2.

b^2 = a^2/5 ( 5divides a^2)

let a = 5 k

b^2 = 25k^2/5

b^2 = 5k^2

b^2/5=k^2 (5 divides b^2 )

therefore 5 is the common factor of a and b

our contradiction fact that a and b are co prime

so our assumption was wrong

root 5 is irrational number .