Radical expressions

Definition

Radical expressions are algebraic expressions that include a root symbol, such as square roots, cube roots, and higher-order roots. They can often be simplified or manipulated using properties of exponents and radicals.

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. Radicals can be converted to expressions with rational exponents, e.g., \(\sqrt[n]{a} = a^{1/n}\).
3. Simplifying radical expressions often involves factoring out perfect squares (or cubes, etc.).
4. The product property of radicals states that \(\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}\).
5. Rationalizing the denominator means eliminating radicals from the denominator by multiplying by an appropriate form of one.

Review Questions

• How do you express the cube root of \(8\) using rational exponents?
• What is the simplified form of \(\sqrt{50}\)?
• Explain how to rationalize the denominator in the expression \(\frac{5}{\sqrt{2}}\).

Related terms

Square Root:

A value that, when multiplied by itself, gives the original number. Represented as \(\sqrt{x}\).

Rational Exponent:

An exponent that is a fraction, where the numerator represents a power and the denominator represents a root.

Radical Equation: An equation in which the variable is under a radical.