Question

√7 is a rational number or not​

Answer 1

Answer:

no it isnt

Step-by-step explanation:

because its decimal expansion is non terminating and non repeating

hope this helps you

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Answer 2

Answer:

√7 is not rational, it is irrational!

Proof,

Let us assume that √7 is rational. Then, there exist co-prime positive integers a and b such that

√7 = a/b

a = b√7

Squaring on both sides, we get

a^2 = 7b^2

Therefore, a^2 is divisible by 7 and hence, a is also divisible by 7.

so, we can write a=7p, for some integer p.

Substituting for a, we get 49p^2 = 7b^2=> b^2 = 7p^2

This means, b^2 is also divisible by 7 and so, b is also divisible by 7.

Therefore, a and b have at least one common factor, i.e., 7.

But, this contradicts the fact that a and b are co-prime.

Thus, our supposition is wrong.

Hence, √7 is irrational number.