Square Root:
The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the value that, when squared, equals the given number. The symbol for square root is √.

For example:
- The square root of 9 is 3 because 3 multiplied by itself (3 x 3) equals 9.
- The square root of 25 is 5 because 5 multiplied by itself (5 x 5) equals 25.

Cube Root:
The cube root of a number is a value that, when multiplied by itself twice, gives the original number. It is the opposite operation of cubing. The symbol for cube root is ∛.

For example:
- The cube root of 8 is 2 because 2 multiplied by itself twice (2 x 2 x 2) equals 8.
- The cube root of 27 is 3 because 3 multiplied by itself twice (3 x 3 x 3) equals 27.

Key Points:
- The square root of a number is the value that, when squared, equals the given number.
- The cube root of a number is the value that, when multiplied by itself twice, equals the given number.
- The symbol for square root is √ and for cube root is ∛.
- Square root is denoted as √number, while cube root is denoted as ∛number.
- Square root is used to find the side length of a square when the area is known.
- Cube root is used to find the side length of a cube when the volume is known.
- Square roots and cube roots can be calculated using calculators or by using manual methods such as prime factorization.

Conclusion:
Square roots and cube roots are mathematical operations used to find the value that, when multiplied by itself or itself twice, equals a given number. The square root is denoted by the symbol √ and the cube root is denoted by ∛. Square roots are used to find the side length of a square, while cube roots are used to find the side length of a cube. These operations can be calculated using calculators or by using manual methods such as prime factorization.