7.3 Radicals and Rational Exponents

Notes

• $\displaystyle \sqrt{a}$ is the nonnegative number whose square is $a$. $\displaystyle \sqrt[3]{a}$ is the cube root.
• Simplify by pulling out perfect squares: $\displaystyle \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$.
• Rational exponents: $\displaystyle a^{\frac{1}{n}} = \sqrt[n]{a}$ and $\displaystyle a^{\frac{m}{n}} = (\sqrt[n]{a})^m$. For example, $\displaystyle 8^{\frac{2}{3}} = (\sqrt[3]{8})^2 = 4$.
• The sum of a rational and an irrational number is irrational.