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### Exercise 5.1 class 8 solution-perfect square number

A perfect square is a number that can be expressed as the product of an integer with itself. In other words, if you take the square root of a perfect square, you will get an integer as the result. For example:

- 1 is a perfect square because 1 = 1 * 1 (the square root of 1 is 1).
- 4 is a perfect square because 4 = 2 * 2 (the square root of 4 is 2).
- 9 is a perfect square because 9 = 3 * 3 (the square root of 9 is 3).
- 16 is a perfect square because 16 = 4 * 4 (the square root of 16 is 4).

In general, if a positive integer “n” can be expressed as “n = a * a,” where “a” is also a positive integer, then “n” is a perfect square. Perfect squares are a subset of square numbers and have a special property of having integer square roots.

### Exercise 5.1 class 8 solution-properties of square number

Square numbers have several interesting properties and characteristics:

- Definition: A square number is a number that can be expressed as the product of an integer with itself. In mathematical notation, a square number is often denoted as n^2, where n is an integer.
- Perfect Squares: Square numbers are also known as perfect squares. These are the numbers that result from squaring an integer. For example, 1, 4, 9, 16, and 25 are all square numbers.
- Integer Square Roots: The square root of a square number is an integer. For example, the square root of 9 is 3, and the square root of 16 is 4.
- Patterns: When you list square numbers, you can observe patterns. The squares of consecutive integers increase by consecutive odd integers. For example, 1, 4, 9, 16, 25, and so on. The difference between consecutive squares is always an odd number (2, 5, 7, 9, …).
- Sum of Consecutive Odd Numbers: Square numbers can also be expressed as the sum of consecutive odd numbers. For example, 16 is the sum of the first four odd numbers (1 + 3 + 5 + 7).
- Pythagorean Triples: Square numbers are often related to Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the Pythagorean theorem: a^2 + b^2 = c^2. The numbers 3, 4, and 5 form a Pythagorean triple since 3^2 + 4^2 = 5^2.

### Exercise 5.1 class 8 solution- square no. 1 to 30

Here are the square numbers from 1 to 30:

- 1^2 = 1
- 2^2 = 4
- 3^2 = 9
- 4^2 = 16
- 5^2 = 25
- 6^2 = 36
- 7^2 = 49
- 8^2 = 64
- 9^2 = 81
- 10^2 = 100
- 11^2 = 121
- 12^2 = 144
- 13^2 = 169
- 14^2 = 196
- 15^2 = 225
- 16^2 = 256
- 17^2 = 289
- 18^2 = 324
- 19^2 = 361
- 20^2 = 400
- 21^2 = 441
- 22^2 = 484
- 23^2 = 529
- 24^2 = 576
- 25^2 = 625
- 26^2 = 676
- 27^2 = 729
- 28^2 = 784
- 29^2 = 841
- 30^2 = 900

These are the squares of the numbers from 1 to 30. Each number on the left represents an integer, and the number on the right is the square of that integer.

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### Exercise 5.1 class 8 solution-solution pdf

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