The problem states that the product of a number and its half is $72$. We need to find the number.

1. Problem Description

The problem states that the product of a number and its half is $72$. We need to find the number.

2. Solution Steps

Let the number be $x$.

Its half is $\frac{x}{2}$.

The product of the number and its half is given by $x \cdot \frac{x}{2}$.

We are given that the product is equal to $72$. Therefore, we can write the equation:

$x \cdot \frac{x}{2} = 72$

Multiplying both sides by 2, we get:

$x^2 = 72 \cdot 2$

$x^2 = 144$

Taking the square root of both sides, we get:

$x = \pm \sqrt{144}$

$x = \pm 12$

Therefore, the number can be either $12$ or $-12$.

3. Final Answer

The number is $12$ or $-12$.