We are asked to order the numbers $\sqrt{72}$, 8, and 9 from least to greatest without using a calculator.

1. Problem Description

We are asked to order the numbers $\sqrt{72}$, 8, and 9 from least to greatest without using a calculator.

2. Solution Steps

First, we can express each number as a square root.

$8 = \sqrt{8^2} = \sqrt{64}$.

$9 = \sqrt{9^2} = \sqrt{81}$.

Now we have $\sqrt{72}$, $\sqrt{64}$, and $\sqrt{81}$. Since the square root function is increasing for positive numbers, we can compare the values inside the square roots to determine the order. We have $64 < 72 < 81$, so $\sqrt{64} < \sqrt{72} < \sqrt{81}$.

Therefore, $8 < \sqrt{72} < 9$.

3. Final Answer

The numbers in order from least to greatest are 8, $\sqrt{72}$, 9.