Question

Prove that√5 is irrational​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

to prove that √5 is irrational

let's assume that√5is rational

so we will find two co primes A and B

such that

√5=a/b

b√5=a

5b^2=a^2. (squaring on both sides)

since a^2 divides 5

so a also divides

now! let's

a=5c for some integer c

a^2=25c^2

5b^2=a^2

5b^2=25c^2

b^2=5c^2

which mean that b also divides 5

but this contradict the fact a and b are co primes

this contradiction ha arisen due to our assumption that√5 is rational