Radicals

A radical is a mathematical symbol that denotes the root of a number. The most commonly used radical is the square root, but radicals can denote any root like the cube root, fourth root, and so forth.

Definition

The radical symbol is √. When used alone, it denotes the square root. The square root of a number a is a number b such that b^2 = a. For example, the square root of 9 is 3 because 3^2 = 9.

For roots other than square roots, a number called the index is placed in the V of the radical symbol. For instance, the cube root of 8 is written as ∛8 and equals 2, because 2^3 = 8.

Properties

Here are some important properties of radicals:

1. Product of Radicals: √(a*b) = √a * √b. This property states that the square root of a product is the product of the square roots.
2. Quotient of Radicals: √(a/b) = √a / √b. This property states that the square root of a quotient is the quotient of the square roots.
3. Power of a Radical: (√a)^n = √(a^n). This property states that a power of a square root is the square root of the power.

Applications

Radicals are used in various fields of mathematics, including algebra, calculus, and trigonometry. They are used to solve equations, calculate distances, and measure areas and volumes, among other things. In real-world terms, radicals often appear in scientific, engineering, and financial calculations.