Question

prove that under root 5 is irrational

Answer 1

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Answer 2

Answer:

Step-by-step explanation:Let us assume on the contrary that √5 is irrational number.

Then , therapy exist co-prime positive integers a and b such that

√5=a/b

5b^2=a^2

5/a^2.        [5/5b^2]

5/a.    (i)

a=5c for some positive integer c

a^2 =25c^2

5b^2=25c^2

b^2=5c^2

5/b^2

5/b.     (i)

From i and ii, we find that a and b have at least  5 as a common factor. This contradicts the fact that a and b are co prime.

Hence, √5 is irrational number.