Question

Which is the correct classification of StartRoot 18 EndRoot?

irrational number, non-repeating decimal
irrational number, terminating decimal
rational number, terminating decimal
rational number, non-repeating decimal

Answer 1

To classify \( \sqrt{18} \):

1. We first simplify \( \sqrt{18} \):
\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]

2. Since \( \sqrt{2} \) is an irrational number, \( 3\sqrt{2} \) is also irrational.

3. An irrational number cannot be expressed as a fraction (ratio of two integers) and its decimal representation is non-repeating and non-terminating.

Given this, \( \sqrt{18} \) is classified as an **irrational number, non-repeating decimal**.