SQUARE ROOT & CUBE ROOT -
In mathematics, a root refers to a value that, when raised to a certain exponent, yields a given result. The most common types of roots are square roots (when the exponent is 1/2), cube roots (when the exponent is 1/3), and higher-order roots. Roots are the inverse operation of exponents, so taking a root "undoes" the effect of raising a number to a power.
Let's look at some specific types of roots:
2. Cube Root:- The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted by the radical symbol with a little 3 in the index.
For any real number a, the cube root is represented as: ∛a
Example: ∛8 = 2 because 2 × 2 × 2 = 8.
3. nth Root:- The nth root of a number is a value that, when multiplied by itself n times, gives the original number. It is denoted by the radical symbol with n in the index. For any real number a and a positive integer n, the nth root is represented as: n√a
Example: 4√16 = 2 because 2 × 2 × 2 × 2 = 16.
Similarly, 3√27 = 3 because 3 × 3 × 3 = 27.
Roots are often used in various mathematical calculations, scientific formulas, and engineering problems. They have applications in calculus, algebra, geometry, and other fields.