RD Sharma Solutions for Class 8 Maths Chapter 3- Squares and Square Roots are available here with clear and simple explanations. Subject experts have explained each concept in an easy-to-understand way, keeping in mind the learning level of students.
These RD Sharma solutions include helpful tips, shortcut methods, and practical examples to make solving the exercises simple and quick. By practising these RD SHarma solutions class 8, students can improve their understanding and aim for high marks in their annual exams.
In this chapter, students will also learn how to check if a number is a perfect square using simple methods. All answers are explained step by step for better understanding. Students can easily download the exercise-wise solutions through the provided links.
RD Sharma Solutions Class 8 Maths Squares and Square Roots - Free PDF Download
At Home-Tution, students can access Class 8 Maths Revision Notes, important formulas, and key questions. They can also refer to the complete Class 8 Maths Syllabus, along with sample papers and previous years’ question papers to prepare effectively and score higher marks in exams.
Access Answers to Maths RD Sharma Solutions for Class 8 Chapter 3
Question: Which of the following numbers are perfect squares?
(i) 484
(ii) 625
(iii) 576
(iv) 941
(v) 961
(vi) 2500
Solutions:
(i) 484
√484 = 22
22 × 22 = 484
Yes, 484 is a perfect square.
(ii) 625
√625 = 25
25 × 25 = 625
Yes, 625 is a perfect square.
(iii) 576
√576 = 24
24 × 24 = 576
Yes, 576 is a perfect square.
(iv) 941
Let's check:
√941 ≈ 30.69 (Not a whole number)
30 × 30 = 900 and 31 × 31 = 961, but 941 lies between these.
No, 941 is not a perfect square.
(v) 961
√961 = 31
31 × 31 = 961
Yes, 961 is a perfect square.
(vi) 2500
√2500 = 50
50 × 50 = 2500
Yes, 2500 is a perfect square.
Question: Find the smallest number by which the given number must be multiplied so that the product is a perfect square:
(i) 23805
(ii) 12150
(iii) 7688
Solutions:
(i) 23805
Step 1: Prime factorization:
23805 = 5 × 3² × 23²
Step 2: Unpaired factor: 5
Answer: Multiply by 5 to make it a perfect square.
(ii) 12150
Step 1: Prime factorization:
12150 = 2 × 3⁵ × 5²
Step 2: Unpaired factors: 2 and 3
Answer: Multiply by 6 (2 × 3) to make it a perfect square.
(iii) 7688
Step 1: Prime factorization:
7688 = 2³ × 31²
Step 2: Unpaired factor: 2
Answer: Multiply by 2 to make it a perfect square.
Question: Show that each of the following numbers is a perfect square. Also find the number whose square is the given number in each case:
(i) 1156
(ii) 2025
(iii) 14641
(iv) 4761
Solutions:
(i) 1156
√1156 = 34
34 × 34 = 1156
Yes, 1156 is a perfect square.
Number whose square is 1156 = 34
(ii) 2025
√2025 = 45
45 × 45 = 2025
Yes, 2025 is a perfect square.
Number whose square is 2025 = 45
(iii) 14641
√14641 = 121
121 × 121 = 14641
Yes, 14641 is a perfect square.
Number whose square is 14641 = 121
(iv) 4761
√4761 = 69
69 × 69 = 4761
Yes, 4761 is a perfect square.
Number whose square is 4761 = 69
Question: Which of the following numbers are perfect squares?
11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121
Solution:
(i) 11
√11 = 3.3166 (Not an integer)
11 is not a perfect square.
(ii) 12
√12 = 3.464 (Not an integer)
12 is not a perfect square.
(iii) 16
√16 = 4 (Whole number)
16 is a perfect square because 4 × 4 = 16.
(iv) 32
√32 = 5.656 (Not an integer)
32 is not a perfect square.
(v) 36
√36 = 6 (Whole number)
36 is a perfect square because 6 × 6 = 36.
(vi) 50
√50 = 7.07 (Not an integer)
50 is not a perfect square.
(vii) 64
√64 = 8 (Whole number)
64 is a perfect square because 8 × 8 = 64.
(viii) 79
√79 = 8.888 (Not an integer)
79 is not a perfect square.
(ix) 81
√81 = 9 (Whole number)
81 is a perfect square because 9 × 9 = 81.
(x) 111
√111 = 10.535 (Not an integer)
111 is not a perfect square.
(xi) 121
√121 = 11 (Whole number)
121 is a perfect square because 11 × 11 = 121.
Question: Which of the following triplets are Pythagorean?
(i) (8, 15, 17)
(ii) (18, 80, 82)
(iii) (14, 48, 51)
(iv) (10, 24, 26)
(v) (16, 63, 65)
(vi) (12, 35, 38)
Solution:
(i) (8, 15, 17)
LHS = 82 + 152
= 289
RHS = 172
= 289
LHS = RHS
The given triplet is a Pythagorean.
(ii) (18, 80, 82)
LHS = 182 + 802
= 6724
RHS = 822
= 6724
LHS = RHS
The given triplet is a Pythagorean.
(iii) (14, 48, 51)
LHS = 142 + 482
= 2500
RHS = 512
= 2601
LHS ≠ RHS
The given triplet is not a Pythagorean.
(iv) (10, 24, 26)
LHS = 102 + 242
= 676
RHS = 262
= 676
LHS = RHS
The given triplet is a Pythagorean.
(v) (16, 63, 65)
LHS = 162 + 632
= 4225
RHS = 652
= 4225
LHS = RHS
The given triplet is a Pythagorean.
(vi) (12, 35, 38)
LHS = 122 + 352
= 1369
RHS = 382
= 1444
LHS ≠ RHS
The given triplet is not a Pythagorean.
Benefits of RD Sharma Solutions for Class 8 Maths Chapter 3
- Clear Concept Understanding: The solutions explain concepts like squares, square roots, and methods to find them in a simple, step-by-step manner, making it easy for students to grasp the basics.
- Step-by-Step Explanations: Each answer is explained in detail with clear steps, helping students understand the logic behind each solution rather than just memorizing answers.
- Practice with Variety of Questions: Students get exposure to a variety of problems basic, moderate, and advanced level enhancing their problem-solving skills.
- Boosts Exam Preparation: Regular practice from RD Sharma helps students revise important formulas, tricks, and shortcuts, making it easier to score high marks in exams.
- Improves Calculation Speed: By solving more exercises, students improve their calculation speed and accuracy, which is crucial in timed exams.
- Ideal for Competitive Exams: The chapter builds a strong foundation in basic Maths concepts, useful not only for school exams but also for competitive exams like Olympiads and NTSE.
- Easy Revision Tool: The chapter-wise solutions act as a quick revision guide before exams, allowing students to revise important methods and avoid last-minute confusion.
Also Read:
Frequently Asked Questions
Ans. You can download the Chapter 3 Solutions PDF from educational websites like Home-Tution for free. These PDFs are organized chapter-wise for easy access.
Ans. In Chapter 3, you can identify perfect squares by checking if the square root of a number is a whole number. If it is, the number is a perfect square (e.g., √16 = 4).
Ans. Yes, RD Sharma explains useful tricks like using unit digit patterns, difference of squares, and prime factorization methods to quickly calculate squares and square roots.
Ans. Important questions often include:
- Finding perfect squares
- Simplifying square roots
- Word problems on square roots
- Questions on consecutive numbers
Ans. Yes, RD Sharma provides enough theory, examples, and exercises to thoroughly prepare for school exams and build strong fundamentals in Squares and Square Roots.
Ans. Absolutely, the detailed solutions and practice problems in Chapter 3 help strengthen your basic concepts, making it helpful for both school exams and competitive exams like Olympiads and NTSE.