- Simplify the fraction inside the radical: \(\frac{80}{5} = 16\).
- Calculate the square root: \(\sqrt{16} = 4\).
- Final Answer: \(\boxed{4}\).
Explanation
- Simplifying the Expression
We want to simplify the numerical expression \(\sqrt{\frac{80}{5}}\). First, we evaluate the fraction inside the square root. Dividing 80 by 5, we get \(\frac{80}{5} = 16\). Now, the expression simplifies to \(\sqrt{16}\). Since \(4^2 = 16\), the square root of 16 is 4.
Examples
In architecture or engineering, simplifying square root expressions is essential when calculating dimensions such as diagonals of rectangular rooms or structural supports. For example, if the ratio of two dimensions is \(\frac{80}{5}\), finding the square root of this ratio helps in scaling models or determining structural limits based on geometric proportions. Understanding how to simplify these radicals ensures quick and accurate assessments in real-world measurements.