91Ó°ÊÓ

This will help you prepare for the material covered in the next section. a. Multiply: \(7(x+5)\) b. Multiply: \(\sqrt{7}(x+\sqrt{5})\)

Explain how to simplify \(\sqrt[n]{a^{n}}\) if \(n\) is even and if \(n\) is odd. Give examples with your explanations.

In Exercises \(105-112,\) add or subtract as indicated. Begin by rationalizing denominators for all terms in which denominators contain radicals. $$\frac{5}{\sqrt{2}+\sqrt{7}}-2 \sqrt{32}+\sqrt{28}$$

In Exercises \(111-114\), simplify each evaluation to the form \(a+b i\) Let \(f(x)=12 x-i\) and \(g(x)=6 x+3 i .\) Find \((f g)\left(-\frac{1}{3}\right)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\sqrt[3]{4} \cdot \sqrt[3]{4}=4$$

This will help you prepare for the material covered in the next section. a. Multiply: \((x+5)(6 x+3)\) b. Multiply: \((\sqrt{2}+5)(6 \sqrt{2}+3)\)

Multiply and simplify: $$\frac{10 y}{\sqrt[5]{4 x^{3} y}} \cdot \frac{\sqrt[5]{8 x^{2} y^{4}}}{\sqrt[5]{8 x^{2} y^{4}}}$$

Explain the meaning of the words radical, radicand, and index. Give an example with your explanation.

In Exercises \(111-114\), simplify each evaluation to the form \(a+b i\) $$\text { Let } f(x)=\frac{x^{2}+19}{2-x} . \text { Find } f(3 i)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\sqrt{12}=2 \sqrt{6}$$