Question

determines if the number is rational or irrational

√81
----- ⋅ 1/3
9

Answer 1

To determine if the expression is rational or irrational, we need to simplify it step by step.

1. First, evaluate \(\sqrt{81}\):
\[
\sqrt{81} = 9
\]

2. Next, substitute \(\sqrt{81}\) in the original expression:
\[
\frac{9}{9} \cdot \frac{1}{3}
\]

3. Now simplify \(\frac{9}{9}\):
\[
\frac{9}{9} = 1
\]

4. Then multiply by \(\frac{1}{3}\):
\[
1 \cdot \frac{1}{3} = \frac{1}{3}
\]

Since \(\frac{1}{3}\) is a rational number (it can be expressed as the ratio of two integers), the final result is rational.

Thus, the expression evaluates to a rational number.