Radical expression

Definition

A radical expression is an algebraic expression that includes a square root, cube root, or any higher-order root. It involves the radical symbol (√) and can include variables and constants.

5 Must Know Facts For Your Next Test

1. The principal square root of a non-negative number \(a\) is denoted as \(\sqrt{a}\).
2. A radical expression can be simplified by factoring out perfect squares, cubes, etc., from under the radical sign.
3. Rational exponents provide an alternative way to express radicals: \(\sqrt[n]{a} = a^{1/n}\).
4. Adding and subtracting radical expressions requires like radicals, similar to combining like terms.
5. Multiplying and dividing radical expressions often involve using properties of exponents and distributing the radicals.

Review Questions

• How do you simplify \(\sqrt{50}\) by factoring out perfect squares?
• What is the equivalent rational exponent form for \(\sqrt[3]{x^2}\)?
• Explain why \(\sqrt{a} + \sqrt{b} ≠ \sqrt{a + b}\).

Related terms

Principal Square Root: The non-negative square root of a non-negative number \(a\), denoted as \(\sqrt{a}\).

Rational Exponent: An exponent that is a fraction, where \(a^{m/n}\) represents the \(n\)-th root of \(a\) raised to the power \(m\).

Like Radicals: Radical expressions that have the same index and radicand, allowing them to be added or subtracted.