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Chapter 0: Problem 148

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?

Short Answer

Expert verified
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 by step solution

01

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 \(4 \cdot 2 = 8\).
02

Evaluate Square Root of Product

In part b, calculate the square root of the product \(16 \cdot 4\) which is \(\sqrt{64} = 8\).
03

Compare Results and Draw a Conclusion

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

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Most popular questions from this chapter

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(x^{4}-16\) is factored completely as \(\left(x^{2}+4\right)\left(x^{2}-4\right)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{2}+36-(x+6)^{2} $$

Simplify by reducing the index of the radical. $$\sqrt[12]{x^{4} y^{8}}$$

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