Last Updated on June 29, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 5 Square and Square Roots. It is a part of Case Study Questions for CBSE Class 8 Maths Series.

Chapter | Square and Square Roots |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 8 |

Subject | Maths |

Useful for | Class 8 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 8 Maths Chapterwise Case Study |

### Case Study Questions on Square and Square Roots

**Questions**

**Passage 1:** During dance practice in school 6570 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row of the square. What is the value depicted from the exercise?

**Difficulty Level: **Medium

Q. 1. How many students were left out in arrangement?

(a) 9

(b) 10

(c) 11

(d) 15

Ans. Option (a) is correct.

Q. 2. What is the number of students forming a square?

(a) 6250

(b) 6760

(c) 6561

(d) 6769

Ans. Option (c) is correct.

Total number = 6570

Number of students left out = 9

Total number of students forming a square = 6570 – 9 = 6561

Q. 3. When arranged for dance, number of students are equal to.

(a) Number of columns

(b) Number of rows

(c) Number of classes

(d) None of these

Ans. Option (b) is correct.

Children are arranged in such order that, Number of students = Number of rows

Q. 4. Find the number of children in each row of the square.

Sol. Total number of children = 6570

Number of students forming square = 6570 – 9 = 6561

Let the number of students in each row be x, So the number of rows will also be = x

Therefore x × x = 6561

This gives, x = 81.

Hence, 81 students are there in each row forming a square.

### Also check

- Square and Square Roots Class 8 Case Study Questions Maths Chapter 5
- Data Handling Class 8 Case Study Questions Maths Chapter 4
- Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3
- Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2
- Rational Numbers Class 8 Case Study Questions Maths Chapter 1

### Download eBooks for CBSE Class 8 Maths Square and Square Roots

### Topics from which case study questions may be asked

- Square Number
- Properties of Square Number
- Patterns of Square Numbers
- Finding the square of Number
- Pythagorean Triplet
- Square Roots (By Repeated Subtraction)
- Finding Square Root through Prime Factorisation
- Finding Square Root by division Method
- Square Roots of Decimals

Square root are the inverse operations of squares.

Case study questions from the above given topic may be asked.

### Frequently Asked Questions (FAQs) on Square and Square Roots Case Study

### Q1: What is a square number?

A1: The square of a number is the product of the number with the number itself.

### Q2: What do you mean by square root?

A2: When a number is multiplied by itself then the product is called square and its inverse operation is called square root.

### Q3: What is the square root of 64?

A3: The square root of 64 is 8.

### Q4: How to find square roots of decimal?

A4: To calculate square root of decimal number bars are put separately on integral part and decimal part. Numerical part which is before decimal is integral part and which is after decimal is decimal part.

In integral part we put bars from the units place close to the decimal and move towards left. And in decimal part also we start from decimal but moves towards right and if needed we can add zero to complete the pair.

### Q5: **What is the perfect square numbers between** 30 and 40?

A5: The perfect square number between 30 and 40 is 36.

### Q6: **Do you think the reverse is also true, i.e., is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.**

A6: No, it is not necessary that the sum of two consecutive positive integers is a perfect square of a number. For example, the sum of 4 and 5 is 9 which is perfect square of 3, but the sum of 3 and 4 is 7 which is not the perfect square of any positive integer.

### Q7: **What are some fundamental facts related to square of a number?**

A7: Some of the fundamental facts are –

(1) If a number has 1 or 9 in units place then it’s square ends in 1.

(2) If a number has 4 or 6 in units place then its square ends in 6.

### Q8: **What are some important properties of square numbers**?

A8: Some properties of square numbers are given below-

(1) A number ending in 2, 3, 7 or 8 at unit’s place is never a perfect square.

(2) A number ending in an odd number of zero’s is never a perfect square. e.g., 40, 4000 etc.

(3) A number ending in an even number of zero may or may not be perfect square e.g., 2500 is a perfect square, but 1700 is not a perfect square.

(4) The square of an even number is even.

(5) The square of an odd number is odd.

### Q9: **Are there any online resources or tools available for practicing **square and square roots** case study questions?**

A9: We provide case study questions for CBSE Class 8 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.