91Ó°ÊÓ

Explain in your own words why possible solutions for radical equations must be checked.

For Problems \(43-54\), find each product and express your answers in simplest radical form. All variables represent nonnegative real numbers. $$ \sqrt{x^{2} y} \sqrt{y} $$

Use a calculator to find a rational approximation of each square root. Express your answers to the nearest hundredth. $$\sqrt{66}$$

Change each radical to simplest radical form. All variables represent positive real numbers. $$\frac{7}{\sqrt{3 y}}$$

Your friend attempts to solve the equation \(3+2 \sqrt{x}=x\) as follows: $$ \begin{array}{r} (3+2 \sqrt{x})^{2}=x^{2} \\ 9+12 \sqrt{x}+4 x=x^{2} \end{array} $$ At this step, she stops and doesn't know how to proceed. What help can you give her?

For Problems \(43-54\), find each product and express your answers in simplest radical form. All variables represent nonnegative real numbers. $$ \sqrt[3]{25 x^{2}} \sqrt[3]{5 x} $$

Change each radical to simplest radical form. All variables represent positive real numbers. $$\sqrt{\frac{3}{x}}$$

Express each radical in simplest radical form. All variables represent nonnegative real numbers. $$-6 \sqrt{72 x^{7}}$$

Use a calculator to find a rational approximation of each square root. Express your answers to the nearest hundredth. $$\sqrt{75}$$

Use a calculator to find a rational approximation of each square root. Express your answers to the nearest hundredth. $$\sqrt{90}$$