Question

prove root 5 is irrational​

Answer 1

Answer:

Root 5 is an irrational number because all roots are irrational

Answer 2

Step-by-step explanation:

let √5 is rational number

these exist two integers a&b where b is not equal to 0

a&b are composite no

a/b =√5

a=√5.b -----------(i)

squaring both side

(a)^2 = (√5.b)^2

a^2= 5b^2[a^2 is divisible by 5]

Let a = 5c [c is an integer]

put value of a in (i) equation

5c = √5.b

square of 5 both side

5×5c^2 =√5×√5.b^2

hence 5 is also divisible b^2

Therefore our esuption is wrong so √5 is an irrational number