Question

Determine if √9 is rational or irrational and give a reason for your answer.

A it is a decimal that terminates

B it is the square root of a perfect square

C it is the square root of a non-perfect square

D it is a decimal that does not repeat or terminate

E it is a decimal that repeats

Answer 1

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**.