Radical expression

Definition

A radical expression is an algebraic expression that includes a root symbol (√). Radicals can include square roots, cube roots, or higher-order roots.

5 Must Know Facts For Your Next Test

1. The most common radical is the square root, denoted as $\sqrt{x}$.
2. Radical expressions can be simplified by factoring out perfect squares or cubes.
3. Rational exponents are another way to express radicals, such as $x^{1/2}$ for $\sqrt{x}$.
4. The properties of radicals include the product rule ($\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$) and the quotient rule ($\sqrt{a/b} = \sqrt{a}/\sqrt{b}$).
5. When solving equations involving radicals, it is important to isolate the radical on one side before squaring both sides to eliminate the radical.

Review Questions

• What does $\sqrt[3]{x}$ represent in terms of rational exponents?
• How would you simplify $\sqrt{50}$?
• Explain how you would solve the equation $\sqrt{x + 3} = x - 1$.

Related terms

Square Root: A number that produces a specified quantity when multiplied by itself, denoted as $\sqrt{x}$.

Cube Root: A number that produces a specified quantity when multiplied by itself twice, denoted as $\sqrt[3]{x}$.

Rational Exponents: Exponents that are fractions, where the numerator represents the power and the denominator represents the root. For example, $x^{1/2} = \sqrt{x}$.