In mathematics, the term radical usually refers to an expression that involves roots, most commonly square roots, but also other roots like cube roots or fourth roots. The radical symbol (√) is used to represent these roots.

Key Points:

1. Square Root (√): The most common radical, used to express the square root of a number. For example, the square root of 9 is written as √9 = 3, because 3² = 9.

2. Cube Root (∛): This is the radical symbol used for cube roots. For example, the cube root of 8 is written as ∛8 = 2, because 2³ = 8.

3. Higher-Order Roots: Radicals can also represent other roots, like the fourth root (⁴√), fifth root (⁵√), etc.

4. Radical Expression: Any expression that includes a radical sign. For example, √x or ∛y.

Example of a Radical Expression:

• √(x + 1) — This represents the square root of the quantity (x + 1).

Radicals can also be simplified or manipulated using certain rules, like:

• √(a * b) = √a * √b
• √(a / b) = √a / √b
• (√a)² = a

If you'd like more examples or a detailed breakdown of how to work with radicals, feel free to ask!

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Here are some follow-up questions:

1. How do you simplify radical expressions?
2. What is the relationship between square roots and exponents?
3. Can you solve equations that contain radicals?
4. What happens when you raise a radical expression to a power?
5. What are irrational numbers, and how are they related to radicals?

Tip: When simplifying radicals, always check if the number under the root can be factored into a perfect square or cube, as this can simplify the expression significantly.