Question

prove that following number irrational are √5​

Answer 1

Answer:

Yes this number is irrational because it is not in the form of p/q

Answer 2

Answer:

√5

let √5 be rational or in the form of p/q where q not equals to 0 and p and q are co prime

√5=p/q ---(1)

squaring both side of (1)

5=p^2/q^2

q^2=p^2/5

therefore, 5 divides p^2

since, 5 divides p

5 is a factor of p

p=5 subsituiting p=5a

q^2=(5a)^2/5 =5×5a^2/5---(2)

q^2/5=a^2

therefore, 5 divides q^2

since, 5 divides q

5 is a factor of q

therefore, we can conclude 5 is a common factor of p and q

this contradiction has arisen due to our wrong asumption √5 is irrational not rational