**RS Aggarwal Class 8 Maths Chapter 3 Ex 3.1 Solutions**: This exercise deals with the basic concepts related to a perfect square & the fundamental explanations of properties of perfect squares. These solutions assist the students in practicing & learning each & every concept as it provides solutions to all questions asked in the textbook. These solutions are organized systematically & cover all solutions to the questions available in this exercise.

In RS Aggarwal Class 8 Maths Chapter 3 Ex 3.1 Solutions, the students find simplified & explained solutions to the difficult problems that make them learn & study much more conveniently. The top Mathematics faculty members have solved the exercise to assist the students with their exam preparation so as to secure good marks in Class 8^{th} Maths final exams. These solutions enable them to clear doubts quickly & also learn the topics more effectively. These solutions are perfect study material the assists the students to understand this exercise in a better way.

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**Download ****RS Aggarwal Class 8 Maths Chapter 3 Ex 3.1 Solutions**

RS Aggarwal Class 8 Maths Chapter 3 Ex 3.1 Solutions

**Important Definition for ****RS Aggarwal Class 8 Maths Chapter 3 Ex 3.1 Solutions**

**Perfect square**

A perfect square is a number that can be expressed as the number of two equal integers. The students will get a perfect square when they multiply two equal integers by each other.

For example: 5 x 5=25

25 is a perfect square because they are multiplying two equal integers (5 & 5) by each other.

It can also be expressed as 5 x 5 as 5^{2} which is known as the term perfect square.

**Properties of perfect squares**

Here are some properties of perfect squares:

1. Property 1: Numbers ending in 2, 3, 7, or 8 is never a perfect square but all the numbers ending in 1, 4, 5, 6, 9, 0 are not square numbers.

2. Property 2: A number ending in an odd number of zeros is never a perfect square.

3. Property 3: The square of an even number is always even.

4. Property 4: The square of an odd number is always odd.

5. Property 5: The square of a proper fraction is smaller than the fraction.

6. Property 6: For every natural number n, we have (n + 1)² – n² = (n + 1 + n)(n + 1 – n) = {(n + 1) + n}. Thus, {(n + 1)² – n²} = {(n + 1) + n}.

7. Property 7: For every natural number n, we have the sum of the first n odd numbers = n²

8. Property 8 (Pythagorean Triplets): Three natural numbers m, n, p is said to form a Pythagorean triplet (m, n, p) if (m² + n²) = p². For each natural number m > 1, we have (2m, m² – 1, m² + 1) as a Pythagorean triplet. For instance: Placing m = 4 in (2m, m² – 1, m² + 1), the students will get (8, 15, 17) as a Pythagorean triplet.

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