Which phrase describes the decimal expansion of the following number?

Question

V27

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

Answer 1

The expression \( \sqrt{27} \) can be simplified as follows:

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

Since \( \sqrt{3} \) is an irrational number, \( 3\sqrt{3} \) is also irrational. The decimal expansion of an irrational number is non-terminating and non-repeating.

Thus, the correct answer is:

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