Question

is \sqrt{7} rational

Answer 1

No, \(\sqrt{7}\) is not a rational number. A rational number is defined as a number that can be expressed as the fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).

The square root of 7 is an irrational number because it cannot be expressed as a fraction of two integers. To show that \(\sqrt{7}\) is irrational, you can use a proof by contradiction, which demonstrates that assuming it is rational leads to a contradiction.

Thus, \(\sqrt{7}\) is an irrational number.