91Ó°ÊÓ

Which values of \(x\) is each radical expression a real number? Express your answer as an inequality or write "all real numbers." $$\sqrt{x-3}\( \)i$$

In Exercises \(75-82\), rationalize each denominator. Simplify, if possible $$\frac{3}{\sqrt{x+3}-\sqrt{x}}$$

Which values of \(x\) is each radical expression a real number? Express your answer as an inequality or write "all real numbers." $$\sqrt{2-x}$$

In Exercises \(69-92,\) simplify using the quotient rule for square roots. $$\frac{\sqrt{54}}{\sqrt{6}}$$

Without using a calculator, simplify the expressions completely. $$\frac{3^{-1} \cdot 3^{\frac{1}{2}}}{3^{-\frac{3}{2}}}$$

In Exercises \(75-82\), rationalize each denominator. Simplify, if possible $$\frac{\sqrt{2}}{\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}}$$

Add or subtract as indicated. You will need to simplify terms before they can be combined. Assume all variables represent nonnegative real numbers. $$5 \sqrt{27 x^{3}}-3 x \sqrt{12 x}$$

Use a graphing utility to solve each radical equation. Graph each side of the equation in the given viewing rectangle. The equation's solution is given by the \(x\) -coordinate of the point \((s)\) of intersection. Check by substitution. $$\begin{aligned} &\sqrt{x}+4=2\\\ &[-2,18,1] \text { by }[0,10,1] \end{aligned}$$

Add or subtract as indicated. You will need to simplify terms before they can be combined. Assume all variables represent nonnegative real numbers. $$7 \sqrt{32 x^{3}}-3 x \sqrt{50 x}$$

Which values of \(x\) is each radical expression a real number? Express your answer as an inequality or write "all real numbers." $$\sqrt{3-x}$$