91Ó°ÊÓ

What are the square roots of \(36 ?\) Explain why each of these numbers is a square root.

Without using a calculator and knowing that \(\sqrt{2} \approx 1.4142\) rationalizing the denominator of \(\frac{1}{\sqrt{2}}\) makes division to obtain a decimal approximation for \(\frac{1}{\sqrt{2}}\) easier to perform. Because 10 and 8 share a common factor of \(2,\) I simplified \(\frac{\sqrt{10}}{8}\) to \(\frac{\sqrt{5}}{4}\)

Make Sense? In Exercises \(90-93,\) determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I use the fact that 1 is the multiplicative identity to both rationalize denominators and rewrite rational expressions with a common denominator.

There is a formula for adding \(\sqrt{a}\) and \(\sqrt{b} .\) The formula is \(\sqrt{a}+\sqrt{b}=\sqrt{(a+b)+2 \sqrt{a b}} .\) Use this formula to add the radicals. Then work the problem again by the methods discussed in this section. Which method do you prefer? Why? $$\sqrt{2}+\sqrt{8}$$

Simplify each radical expression. $$\sqrt[3]{16}$$

In Exercises \(94-97,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{4+8 \sqrt{3}}{4}=1+8 \sqrt{3}$$

Explain why \(\sqrt{-1}\) is not a real number.

Simplify each radical expression. $$\sqrt[3]{32}$$

There is a formula for adding \(\sqrt{a}\) and \(\sqrt{b} .\) The formula is \(\sqrt{a}+\sqrt{b}=\sqrt{(a+b)+2 \sqrt{a b}} .\) Use this formula to add the radicals. Then work the problem again by the methods discussed in this section. Which method do you prefer? Why? $$\sqrt{5}+\sqrt{20}$$

Explain why \(\sqrt[3]{8}\) is 2 . Then describe what is meant by \(\sqrt[n]{a}=b\)