Question

1. Prove that √5 is irrational..​

Answer 1

Answer:

we assume that √5 is rational number and it's simplest form is a/b

thus, a and b are integers that no common factors , except 1 .

√5 = a/b .................(1)

squaring both sides , we get :

5 = a^2/b^2

5b^2 = a^2...............(2)

5 divides a^2

= 5 also divides a

let a = 5c where c is a integer

from equation 2 , we get

5b^2 = (2c^2)

5b^2 = 25 c^2

b^2 = 5c^2

5c^2 = b^2

= 5 divides b^2

5 also divides b

it is clear from above a and b have 5 as common factors.

but , this contradict the fact that a and b have no common factor other than 1.

.

. . √5 is an irrational number.

Answer 2

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