is the square root of 18 rational or irrational

1 answer

The square root of 18 is irrational.

To see why, we can simplify \(\sqrt{18}\):

\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

Since \(\sqrt{2}\) is known to be irrational, \(3\sqrt{2}\) is also irrational. Therefore, \(\sqrt{18}\) is irrational.