91Ó°ÊÓ

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. $$\begin{aligned} &\sqrt{x}+3=5\\\ &[-1,6,1] \text { by }[-1,6,1] \end{aligned}$$

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

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

In Exercises \(69-92,\) simplify using the quotient rule for square roots. $$\sqrt{\frac{72}{y^{20}}}$$

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. $$\begin{aligned} &\sqrt{x^{2}+3}=x+1\\\ &[-1,6,1] \text { by }[-1,6,1] \end{aligned}$$

Multiply as indicated. If possible, simplify any square roots that appear in the product. $$(\sqrt{x}-\sqrt{10})^{2}$$

In Exercises \(69-92,\) simplify using the quotient rule for square roots. $$\sqrt{\frac{300}{y^{30}}}$$

Without using a calculator, simplify the expressions completely. $$25^{\frac{1}{4}} \cdot 25^{-\frac{3}{4}}$$

Multiply as indicated. If possible, simplify any square roots that appear in the product. $$(\sqrt{x}-\sqrt{11})^{2}$$

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. $$\begin{aligned} &4 \sqrt{x}=x+3\\\ &[-1,10,1] \text { by }[-1,13,1] \end{aligned}$$