1. Square:
(i) 2² = 2 × 2 =
(ii) 3² = 3 × 3 =
2. Perfect square: Explain the concept of a perfect square.
Answer (2)
In mathematics, squaring a number means multiplying it by itself, resulting in numbers like 4 from 2² and 9 from 3². A perfect square is an integer that can be expressed as the square of another integer, such as 1, 4, 9, 16, and so on. These concepts highlight how certain numbers are related through multiplication.
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Let's go through the question step by step to understand the concepts of 'square' and 'perfect square'.
Square :
(i) 2 2 = 2 × 2 = 4
(ii) 3 2 = 3 × 3 = 9
A square is the result of multiplying a number by itself. In these examples, 2 2 and 3 2 represent the squares of 2 and 3, respectively.
Perfect Square :
A perfect square is an integer that is the square of an integer. In other words, when you multiply a whole number by itself, the result is called a perfect square. For example:
4 is a perfect square because it is 2 2 ( 2 × 2 = 4 ).
9 is a perfect square because it is 3 2 ( 3 × 3 = 9 ).
Perfect squares are important in mathematics because they help us understand and solve problems related to areas, especially in geometry. They also play a critical role in algebra and number theory.
In summary, understanding the concept of squaring a number and recognizing perfect squares can greatly assist in different areas of mathematics, enhancing problem-solving skills and mathematical reasoning.
