Squares And Square Roots – Complete Guide For Class 8 Chapter 6

Welcome to iPrep, your Learning Super App. Our learning resources for the chapter, Squares and Square Roots in Mathematics Class 8th chapter 6 are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples.

Chapter 6 explores the concepts of squares and square roots. Students learn to identify perfect squares, calculate squares of numbers, and find square roots using methods like prime factorization and division. The chapter squares and square roots also introduces the Pythagorean triplets and their applications.

In Chapter 6 squares and square roots, we explore the fascinating world of squares and square roots, fundamental concepts in mathematics that lay the groundwork for more complex topics. Here, we’ll delve into key concepts, properties, and interesting patterns related to squares and square roots.

Square of a Number

The square of a number is obtained by multiplying the number by itself. For instance:

• 2² = 2×2 = 4
• 5² = 5×5 = 25
• 10² = 10×10 = 100

Perfect Squares

A number is a perfect square if it can be expressed as the square of an integer. For example, n=m² where m is an integer.

Properties of Square Numbers

Now that we have learnt about square numbers we will now see some properties of square numbers.

1. Last Digit Property: The squares of integers end with the digits 0, 1, 4, 5, 6, or 9.
2. Units Digit: Numbers ending in 2, 3, 7, or 8 are never perfect squares.
3. Zeros Property: A perfect square number always has an even number of zeros at its end.
4. Parity Property: The square of an even number is even, and the square of an odd number is odd.

Interesting Patterns in Squares

• Numbers Between Squares: There are 2n non-square numbers between the squares of two consecutive numbers n and n+1.
• Adding Odd Numbers: The sum of the first n odd numbers equals n².

Patterns in Square Numbers

• Pattern I: The sequence 1²,11²,111²,… follows a unique pattern, producing numbers like 121, 12321, 1234321, and so on.
• Pattern II: The sum of digits in numbers like 121, 12321, etc., forms a perfect square.

Finding Squares and Square Roots

• Using Successive Subtraction: Subtract successive odd numbers from the perfect square until you reach zero. The number of subtractions equals the square root.
• Prime Factorization: Factorize the number into prime factors, pair them, and multiply one from each pair.
• Division Method: A systematic approach involving bars over digit pairs and iterative division.
• Square Roots of Decimals: Extend the concept to decimal numbers, ensuring the correct number of decimal places.

Estimating Square Roots

For numbers that are not perfect squares, approximate the square root by identifying the closest perfect squares.

Example: For √35​:

• 25<35<36
• √25 ​= 5 and √36 = 6 
• Thus, √35​ is approximately 6.

This chapter not only strengthens basic mathematical skills but also paves the way for understanding more complex algebraic concepts. Through various methods and interesting patterns, students learn to work with squares and square roots, enhancing their problem-solving abilities and mathematical intuition.