Final answer:
The number in question is 24.
Step-by-step explanation:
The problem states that 3/4th of a number, when multiplied by 3/4th of the same number, equals 324. Let's represent the unknown number as x. The equation can be written as (3/4)x * (3/4)x = 324. Simplifying this equation gives us [(3/4)^2]x^2 = 324.
To solve for x, we can take the square root of both sides of the equation since [(3/4)^2] is a perfect square. This gives us (3/4)x = ±√(324).
Now, we need to consider the positive and negative roots. Taking the positive root gives us (3/4)x = √(324) = 18. Solving for x, we have x = (4/3) * 18 = 24. Similarly, taking the negative root gives us x = -(4/3) * 18 = -24. However, since the problem asks for the number and not its negative value, the number is 24.