Question

1. Prove that
5 is irrational.


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Answer 1

Answer:

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Answer 2

Answer:

Let √5 be rational number.

let √5 = a/b , where b ≠ 0 & a and b are co prime integers.

b√5 = a

sq on both sides.

5b² = a²

therefore, a² is divisible by 5,

that implies a is divisible by 5. -------------eqn 1

so , a = 5m

a² = 25m²

frm eqn 1,

5b² = 25m²

b² = 5m²

therefore b² is divisible by 5

that implies b is divisible by 5. ---------------eqn 2

from eqn 1 & 2,

a and b are divisible by 5,

but we assumed that a & b are co prime Integers

therefore, our assumption is incorrect.

hence, √5 is irrational.

H,P

hope it helped!