RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 Squares and Square Roots
Neha Tanna31 Jul, 2024
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RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4: The Physics Wallah academic team has provided a comprehensive answer for Chapter 3: Squares and Square Roots in the RS Aggarwal class 8 textbook. Read the theory of chapter-3 Squares and Square Roots before attempting to solve all of the numerical problems in exercise-3D.
One must have a thorough understanding of chapter-3 Squares and Square Roots before proceeding with the solution of Exercise-3D. For class 8 maths students, the NCERT textbook is a highly recommended resource for solving numerical problems and referencing NCERT solutions.RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 Squares and Square Roots Overview
RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 focuses on "Squares and Square Roots." Exercise 3.4 is an essential part of this chapter, offering a series of problems designed to enhance students' understanding and proficiency in dealing with squares and square roots. RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 includes a variety of questions that require students to find the squares of numbers, determine the square roots of perfect squares, and solve problems involving the properties of squares and square roots. This section emphasizes conceptual clarity and practical application. Students are often tasked with solving equations that involve square roots, simplifying expressions with squares and square roots, and applying these concepts to solve real-world problems. The problems range from straightforward calculations to more complex word problems, encouraging students to develop a deeper understanding of the subject.RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 PDF
The exercise includes a mix of direct computation problems, word problems, and real-life applications, enhancing students' problem-solving skills and their ability to relate mathematical concepts to everyday situations. By working through this exercise, students strengthen their foundational knowledge of squares and square roots, preparing them for more advanced topics in algebra and geometry. Below we have provided RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 in detail. This chapter will help you to clear all your doubts regarding the chapter. Students are advised to prepare from these RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 before the examinations to perform better.RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 PDF
RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 (Ex 3D)
Below we have provided RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 Squares and Square Roots –Find the square root of each of the following numbers by using the method of prime fraction:
(1) 225
Solution: By prime factorization,
225 = 3 × 3 × 5 × 5 ∴ √225 = (3 × 5) = 15.(2) 441 = 3 × 3 × 7 × 7
∴ √441 = (3 × 7) = 21.(3) 729 = 3 × 3 × 3 × 3 × 3 × 3
∴ √729 = (3 × 3 × 3) = 27.(4) 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
∴ √1296 = (2 × 2 × 3 × 3) = 36.(5) 2025 = 3 × 3 × 3 × 3 × 5 × 5
∴ √2025 = (3 × 3 × 3 × 5) = 45.(6) 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
∴ √4096 = (2 × 2 × 2 × 2 × 2 × 2) = 64.(7) 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
∴ √7056 = (2 × 2 × 3 × 7) = 84.(8) 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5
∴ √8100 = (2 × 3 × 3 × 5) = 90.(9) 9216 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
∴ √9216 = 2 × 2 × 2 × 2 × 2 × 3 = 96.(10) 11025 = 3 × 3 × 5 × 5 × 7 × 7
∴ √11025 = (3 × 5 × 7) = 105.(11) 15876 = 2 × 2 × 3 × 3 × 3 × 3 × 7 × 7
∴ √15876 = (2 × 3 × 3 × 7) = 126.(12) 17424 = 2 × 2 × 2 × 2 × 3 × 3 × 11 ×11
∴ √17424 = (2 × 2 × 3 × 11) = 132.(13) Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root the perfect square so obtained.
Solution: By prime factorization, we get
252 = 2 × 2 × 3 × 3 × 7 So, the given number should be multiplied by 7to make the product a perfect square. New number = 252 × 7 = 1764 ∴ 1764 = 2 × 2 × 3 × 3 × 7 × 7 √1764 = 2 × 3 × 7 = 42(14) Find the smallest number by which 2925 must be divided to obtain a perfect square. Also find the square root of the perfect square so obtained.
Solution: By prime factorization, we get
2925 = 3 × 3 × 5 × 5 × 13 So, the given number should be divided by 13 to make the product a perfect square. New number = 2925 ÷ 13 = 225 ∴ 225 = 3 × 3 × 5 × 5 √225 = 3 × 5 = 15(15) 1225 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Solution: Let the number of row be x.
∴ x 2 = 1225 or, x = √1225 or, x = 5 × 7 = 35 Hence, the number of the rows is 35.(16) The students of a class arranged a picnic. Each student contributed is Rs 1156, find the strength of the class.
Solution: Let the number of students be x.
∴ x 2 = 1156 or, x = √1156 or, x = 2 × 17 = 34(17) Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.
Solution: The least number divisible by each one of 6, 9, 15 and 20 is their LCM.
Now, LCM of 6, 9, 15 and 20 = (2 × 3 × 5 × 3 × 2) = 180. By prime factorization, we get 180 = 2 × 2 × 3 × 3 × 5 To make it perfect square it must be multiplied by 5. Hence, required number = (180 × 5) = 900.(18) Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.
Solution: The least number divisible by each one of 8, 12, 15 and 20 is their LCM.
Now, LCM of 8, 12, 15, 20 = (2 × 2 × 3 × 5 × 2) = 120. By prime factorization, we get 120 = 2 × 2 × 2 × 3 × 5 To make it a perfect square it must be multiplied by (2 × 3 × 5), i.e., 30. Hence, required number = (120 × 30) = 3600.Benefits of RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4
The RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 on Squares and Square Roots offers several benefits to students:Enhanced Understanding : The solutions provide detailed, step-by-step explanations for each problem, helping students understand the underlying concepts of squares and square roots thoroughly.
Practice and Reinforcement : With a variety of problems, students get ample practice, which reinforces their learning and helps them retain the concepts better.
Problem-Solving Skills : The exercise includes different types of questions, from basic calculations to complex word problems, which enhance students' problem-solving skills and analytical thinking.
Error Identification : By comparing their answers with the solutions, students can identify and correct their mistakes, leading to improved accuracy in their work.
Exam Preparation : The solutions align with the curriculum and are designed to prepare students for exams by covering all possible question types that might appear in tests and exams.
Confidence Building : Understanding and solving the problems correctly boosts students' confidence in their mathematical abilities, encouraging them to tackle more challenging problems.
RS Aggarwal Solutions for Class 8 Maths Chapter 3 Exercise 3.4 FAQs
What is a perfect square?
How do you find the square of a number?
What is the square root of a number?
What is the prime factorization method for finding square roots?
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