Question

Is \sqrt{50} rational or irrational

Answer 1

To determine whether \(\sqrt{50}\) is rational or irrational, we can simplify \(\sqrt{50}\):

\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\]

Now, we need to check if \(\sqrt{2}\) is rational or irrational. It is well-known that \(\sqrt{2}\) is an irrational number, meaning it cannot be expressed as a fraction of two integers.

Since \(5\) is rational and \(\sqrt{2}\) is irrational, the product \(5\sqrt{2}\) is also irrational. Therefore, \(\sqrt{50}\) is irrational.

In conclusion, \(\sqrt{50}\) is irrational.