1. The problem is to express a number or expression in terms of radicals, which means using roots such as square roots, cube roots, etc. 2. The general formula for expressing a number in radicals depends on the context, but often involves rewriting expressions using the property $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. 3. Important rules include: - $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ - $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ - Simplify radicals by factoring out perfect powers. 4. For example, to express $\sqrt{50}$ in radicals: $$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$$ 5. This shows the expression in simplest radical form. 6. If you have a fraction like $\frac{1}{\sqrt{3}}$, rationalize the denominator: $$\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{\cancel{\sqrt{3}} \times \cancel{\sqrt{3}}} = \frac{\sqrt{3}}{3}$$ 7. This is the expression in radicals with a rationalized denominator. 8. Always look to simplify radicals by factoring out perfect squares or cubes and rationalize denominators when necessary.