Which phrase describes the decimal expansion of the following number?

Question

√27

A.
a repeating decimal
B.
a non-terminating, non-repeating decimal
C.
a terminating decimal
D.
does not have a decimal expansion

Answer 1

To determine the nature of the decimal expansion of \(\sqrt{27}\), we first simplify the expression:

\[ \sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3} \]

The square root of 3, \(\sqrt{3}\), is an irrational number, which means it cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.

Since \(\sqrt{27} = 3\sqrt{3}\), and \(\sqrt{3}\) is irrational, it follows that \(\sqrt{27}\) also has a non-terminating, non-repeating decimal expansion.

Therefore, the correct answer is:

B. a non-terminating, non-repeating decimal.