Problem 148 - College Algebra

Question

a. Find \(\sqrt{16} \cdot \sqrt{4}\) b. Find \(\sqrt{16 \cdot 4}\) c. Based on your answers to parts (a) and (b), what can you conclude?

Step-by-Step Solution

Answer

a. \(\sqrt{16} \cdot \sqrt{4} = 8\) . b. \(\sqrt{16 \cdot 4} = 8\). c. These results show that the square root of a product and the product of individual square roots yield the same result.

Step 1: Evaluate Square Roots Individually

In part a, you're asked to find \(\sqrt{16} \cdot \sqrt{4}\) . Finding the square root of each number individually gives \(4 \cdot 2 = 8\).

Step 2: Evaluate Square Root of Product

In part b, calculate the square root of the product \(16 \cdot 4\) which is \(\sqrt{64} = 8\).

Step 3: Compare Results and Draw a Conclusion

In both scenarios, the result is 8. This demonstrates that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\) .