Squares, Square Roots, Cubes and Cube Roots

Understanding the concepts of squares, square roots, cubes and cube roots is essential. These concepts play a crucial role in various mathematical operations and problem-solving. As you gear up for the Common Law Admission Test (CLAT), developing a clear grasp of these fundamentals will empower you to tackle quantitative aptitude questions confidently. Let’s explore these concepts in simple terms.

Squares and Square Roots

• Squares: When a number is multiplied by itself, the result is called its square. For example, the square of 3 is 3 multiplied by 3, which equals 9.
• Square Roots: The square root of a number is the value that, when multiplied by itself, gives the original number. For instance, the square root of 25 is 5 because 5 multiplied by 5 equals 25.

Cubes and Cube Roots

• Cubes: A cube of a number is found by multiplying the number by itself twice. For example, the cube of 2 is 2 × 2 × 2, which equals 8.
• Cube Roots: The cube root of a number is the value that, when multiplied by itself twice, gives the original number. If we take the cube root of 27, we get 3 because 3 × 3 × 3 equals 27.

Understanding the Importance

Understanding squares, square roots, cubes and cube roots is beneficial in various real-world scenarios and mathematical problems. These concepts appear in calculations, geometry and even scientific calculations.

Examples

Let’s take a look at a few examples to solidify our understanding:

• Squares: The square of 7 is 7 × 7 = 49.
• Square Roots: The square root of 16 is 4 because 4 × 4 = 16.
• Cubes: The cube of 4 is 4 × 4 × 4 = 64.
• Cube Roots: The cube root of 27 is 3 because 3 × 3 × 3 = 27.

Strategies for Quick Calculation

To make calculations involving squares, square roots, cubes and cube roots easier, consider these strategies:

• Memorise Squares and Cubes: Remembering the squares of numbers up to 10 and the cubes of numbers up to 5 can save time in calculations.
• Estimation: When calculating square roots or cube roots, estimate the answer to see if it’s close to a whole number. This can help you identify potential mistakes.
• Patterns: Notice patterns in square and cube values. For instance, squares of consecutive numbers have a specific pattern (e.g., 1² = 1, 2² = 4, 3² = 9 and so on).