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Learning Poster: Perfect Square and Square Root | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download
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FAQs on Learning Poster: Perfect Square and Square Root - Mathematics Class 8- New NCERT (Ganita Prakash)
| 1. What is a perfect square and how can it be identified? |  |
Ans. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, and 25 are perfect squares because they can be written as 1², 2², 3², 4², and 5² respectively. To identify a perfect square, you can take the square root of the number; if the result is an integer, then the original number is a perfect square.
| 2. How do you calculate the square root of a number? | |
Ans. The square root of a number is a value that, when multiplied by itself, gives the original number. To calculate the square root, you can use various methods such as prime factorization, estimation, or using a calculator. For example, to find the square root of 36, you can determine that 6 × 6 = 36, so the square root of 36 is 6.
| 3. What are some properties of perfect squares? | |
Ans. Perfect squares have several interesting properties. They are always non-negative integers, and their square roots are whole numbers. Additionally, the difference between two consecutive perfect squares can be expressed as the sum of the two integers that are being squared. For instance, the difference between 4 (2²) and 9 (3²) is 5, which is 2 + 3.
| 4. Can negative numbers be perfect squares? | |
Ans. No, negative numbers cannot be perfect squares. By definition, a perfect square is formed by multiplying a number by itself, and since the square of any real number (positive or negative) is always non-negative, perfect squares must be zero or positive integers.
| 5. What is the significance of perfect squares and square roots in mathematics? | |
Ans. Perfect squares and square roots play a crucial role in various branches of mathematics, including algebra, geometry, and number theory. They are essential in solving quadratic equations, understanding geometric shapes like squares and rectangles, and in real-world applications such as calculating areas and optimizing problems. Understanding these concepts helps build a solid foundation for more advanced mathematical topics.
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