[Maths Class Notes] on Squares and Square Roots Pdf for Exam

After you are done with the preceding chapters, you will proceed to learning about squares and square roots in your CBSE Maths Class 8 Chapter 6 curriculum. This is one of the most interesting chapters that requires you to concentrate properly. Along with the various mathematical solutions, this chapter also helps a student understand the various properties of square roots. Additionally, you can learn various tips and tricks regarding the calculation of perfect squares and square roots.What are Perfect Squares?When you multiply any whole number with itself, you get a result, which is known as the perfect square of the first number.Let us consider an example to clarify what a perfect square signifies. Suppose, the starting number is 12. When multiplied by itself or squared, the resulting figure is 144. You can say that 144 is the perfect square for the number 12.Important Properties of all Square NumbersThe key to understanding squares and square roots is to first gauge a few common characteristics, which are shared by all square numbers. Learning them can help your calculations greatly – If a number has 3, 8, 2 or 7 in its units’ place, then it cannot be a perfect square number.Numbers with 0, 4, 1, 6, 5 and 9 may or may not be perfect squares. For example, 36 has six in the units’ place and is the square of the number 6. Nevertheless, 136 also has six in the units’ place but is not a perfect square. Its square root is 11.66.Square Root CalculationWhen you know the square of a number but do not know the number itself, the procedure to discover this number is known as square root. It is basically the inverse function of squaring a figure.Thus, now that you know the relationship between square and square roots, here is a few tips that should assist you in estimating square root from a given figure.Useful NotesYou can easily calculate how many digits the square root of a given perfect square possesses by a simple formula.Consider ‘x’ as the number of digits in the perfect square. Number of digits (n) in the square root is equal to x/2, where x is even. If x is odd, n = x+1x+1x + 1/2.For example, let us consider the number 625. Here, x = 3, which is an odd number. Therefore, n = 3+13+13 + 1/2 = 2. We can confirm this assertion as the square root of 625 is 25, which has two digits.Estimating the Value of Square RootsIf you are in a hurry and need an approximate square root value, you can estimate the same using a simple technique. To demonstrate the same, let us take the number 671 as an example. It is not a perfect square. However, to estimate, let us consider the two perfect square numbers closest to 671, which are 625 and 676. Since 671 is closer to 676, whose square root is 26, you can assume that the square root of 676 is approximately 26 as well. Calculating Square Root Using Subtraction MethodIn squares and square roots chapter, you will also learn about another method to derive square root from a perfect square. Suppose, the number is 25. The number of subsequent odd number subtractions you can undertake from the given number before reaching 0 should be its square root.25 – 1 = 2424 – 3 = 2121 – 5 = 1616 – 7 = 99 – 9 = 0As you can see, there are 5 such subtractions before reaching 0. Therefore, we can say that the square root of 25 is 5. Multiple Choice QuestionQ. Which of the following numbers will produce even squares?981783268547Ans. (c) 268Are you facing difficulty understanding any section of the squares and square roots chapter? Well, we at can help you with all your preparations. Our online classes and excellent study materials are designed to give students an edge. Moreover, with doubt clearing sessions, our students can attain extensive clarity on each topic. Come and join for a class on perfect squares and square roots!

Need of Square and Square Roots

Not only in everyday math but also in advanced stages of life square and square roots are applicable. square roots are not only important topics for students but this is applied by engineers at their work. square and square roots are applicable for getting quadratic equations and solving Pythagoras theorem. Pythagoras Theorem is based on square roots of a number. There is a need for square and square roots because it is not only applicable to math but it is very useful for deriving standard deviation in statistics; it is useful in Algebra as well as in geometry.

Square and square roots are really very important for math students not only at school level but also during preparation of Neet for exams. square and square roots are introduced to the students from class 7 onwards but students learn more about them in class 8. CBSE books of Standard 8 explains this particular topic in detail:

 The contents of the course book are:

1.  Rational numbers

2.  Linear equations in one variable

3.  Understanding quadrilaterals

4.  Practical geometry

5.  Data handling

6.  Square and square roots

7.  Cubes and cube roots

8.  Comparing quantities

9.  Algebraic expressions and identities

10.  Visualizing solid shapes

11.  Area of polygons surface

12.  Area and volume of solids

13.  Exponents and powers

14.  Direct and Inverse proportions

15.  Factorization introduction to graphs

16.  Playing with numbers.

The Chapter 6 Explains Regarding:

 squares of a number, square of a rational number, square of a large number, finding the product of two consecutive odd-even integers, finding a Pythagorean triplet, it also explains regarding finding square roots by various methods, finding square root through repeated subtraction, finding square root through prime factorization, finding square root by division method, properties of square root and approximate square root by division method.