Powers and Roots in 11-Plus Mathematics The topic of Powers and Roots is essential in 11-plus Mathematics, focusing on understanding and calculating squares, cu...
The topic of Powers and Roots is essential in 11-plus Mathematics, focusing on understanding and calculating squares, cubes, square roots, and cube roots. This topic helps students develop a strong foundation in number operations, which is crucial for their mathematical journey.
A square of a number is the result of multiplying that number by itself. For example, the square of 3 is 3² = 9. Similarly, a cube of a number is the result of multiplying that number by itself twice. For instance, the cube of 2 is 2³ = 8.
Students should be able to recognise common square and cube numbers:
Index notation is a concise way to express powers. For example, instead of writing 2 × 2 × 2, we can write 2³. Understanding index notation is crucial for simplifying calculations and solving problems efficiently.
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. The symbol for square root is √.
A cube root is a value that, when used in a multiplication three times, results in the original number. For instance, the cube root of 27 is 3 since 3 × 3 × 3 = 27. The symbol for cube root is ∛.
Students will encounter various problems involving powers and roots. Here are some example problems:
Problem 1: What is the square of 7?
Solution:
Problem 2: What is the cube root of 64?
Solution:
By mastering the concepts of powers and roots, students will enhance their mathematical skills and prepare effectively for the 11-plus examination.