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Magazine Problem 2
Show that the quotient of two irrational numbers can be either rational or irrational.
Problem 3
In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ \sqrt{a}=5 $$
Problem 4
In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{5} \cdot \sqrt{45} $$
Problem 5
In \(3-14,\) determine whether each of the numbers is rational or irrational. $$ 3 \pi $$
Problem 6
Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{4}{2 \sqrt{3}}\)
Problem 8
Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{4}{8 \sqrt{6}}\)
Problem 9
Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{12}{\sqrt{27}}\)
Problem 10
In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ \sqrt{1+x}=3 $$
Problem 13
In \(3-14,\) determine whether each of the numbers is rational or irrational. $$ \frac{\pi}{\pi} $$
Problem 13
In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{\sqrt{27 b}}{\sqrt{6 b^{2}}} $$
