Question

examine
$\sqrt{7}$
is rational or irrational ​

Answer 1

Hey buddy ✌✌✌

√7 is an irrational number.

Hope this helps you...!!! ✌✌✌✌✌

Answer 2

Answer:

√7 is irrational.

Step-by-step explanation:

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

a² = 7b²

Therefore, a² 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

49p² = 7b²

=> b² = 7p²

This means b² 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.

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