Class 8 Maths — Chapter 1: A SQUARE AND A CUBE

What you'll learn

• ▸Factors and Perfect Squares
• ▸Definition and Notation of Square Numbers
• ▸Properties of Units Digits in Perfect Squares
• ▸Properties of Zeros and Parity in Perfect Squares
• ▸Squares as Sums of Consecutive Odd Numbers
• ▸Introduction to Square Roots
• ▸Non-Perfect Squares Between Consecutive Squares
• ▸Relation between Square and Triangular Numbers

Chapter Summary

--- PAGE 1 --- A SQUARE AND A CUBE Queen Ratnamanjuri had a will written that described her fortune of *ratnas* (precious stones) and also included a puzzle. Her son Khoisnam and their 99 relatives were invited to the reading of her will. She wanted to leave all of her *ratnas* to her son, but she knew that if she did so, all their relatives would pester Khoisnam forever. She hoped that she had taught him everything he needed to know about solving puzzles. She left the following note in her will— “I have created a puzzle. If all 100 of you answer it at the same time, you will share the *ratnas* equally. However, if you are the first one to solve the problem, you will get to keep the entire inheritance to yourself. Good luck.” The minister took Khoisnam and his 99 relatives to a secret room in the mansion containing 100 lockers. The minister explained— “Each person is assigned a number from 1 to 100. * Person 1 opens every locker. * Person 2 toggles every 2nd lo…

Practice Questions from this Chapter

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1. Explain square numbers simply. Get Solution →
2. Show prime number patterns. Get Solution →
3. Solve number factor problems. Get Solution →
4. In the story, who is assigned the task of opening every single locker at the start of the puzzle? Get Solution →
5. According to the chapter, what is a number called if it can be expressed as the product of a number with itself? Get Solution →
6. What are the squares of natural numbers, like 1, 4, 9, and 16, called? Get Solution →
7. Which of the following digits can a perfect square number NOT end in? Get Solution →
8. What is the sum of the first four consecutive odd numbers (1 + 3 + 5 + 7)? Get Solution →

Did you know?

• 💡 The largest known prime number has over 24 million digits.
• 💡 The sum of consecutive odd numbers, starting from 1, always results in a perfect square.
• 💡 The number 1 is neither a prime number nor a composite number.
• 💡 Ancient Babylonians used a base-60 number system, influencing our time and angles.
• 💡 All prime numbers, except 2 and 3, are next to a multiple of six.

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