To determine whether \( \sqrt{9} \) is rational or irrational, we first calculate the value of \( \sqrt{9} \):
\[ \sqrt{9} = 3 \]
Since 3 is a whole number, it is classified as a rational number. A rational number can be expressed as the ratio of two integers (in this case, \( \frac{3}{1} \)).
Now, let's consider the options provided:
- A: it is a decimal that terminates. (True, since 3 can be represented as 3.0)
- B: it is the square root of a perfect square. (True, since 9 is indeed a perfect square)
- C: it is the square root of a non-perfect square. (False, because 9 is a perfect square)
- D: it is a decimal that does not repeat or terminate. (False, as 3 is a terminating decimal)
- E: it is a decimal that repeats. (False, as 3 is not repeating)
Among these options, the most appropriate reason for indicating that \( \sqrt{9} \) is rational is:
B: it is the square root of a perfect square.
Thus, the answer is B.
1 answer