# Square Roots and Cube Roots

## Square Roots and Cube Roots

• The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3*3=9.
• The symbol for the square root is √.
• Every positive number has two square roots, one positive and one negative. For example, the square roots of 9 are 3 and -3 because (33=9) and (-3-3=9)
• A square root that is a whole number is called a perfect square. Examples of perfect squares include 1, 4, 9, 16, 25, etc.
• A square root that is not a whole number is irrational, and it can’t be exactly represented as a fraction or decimal. These square roots are usually rounded to a certain number of decimal places.
• The cube root of a number is a value that, when multiplied by itself twice, gives the original number. For example, the cube root of 27 is 3, because 333=27.
• The symbol for the cube root is ∛.
• Every real number has only one real cube root. For example, the cube root of -27 is -3, because -3-3-3=-27.
• A cube root that is a whole number is called a perfect cube. Examples of perfect cubes include 1, 8, 27, 64, 125, etc.
• Learning to manually calculate square roots and cube roots can be useful, but for complex calculations, using a calculator can more accurately and quickly provide answers.
• Understanding square roots and cube roots can be helpful when dealing with quadratic or cubic equations or in understanding Pythagorean theorem in geometry.

Practice and well-conceptualised examples are key to understanding and becoming more familiar with the concepts of square roots and cube roots. Remember to revise regularly for better retention of the concept.