Important Questions Class 8 Maths Chapter 1 A Square and A Cube
Important Questions Class 8 Maths Chapter 1 A Square and A Cube
A Square and A Cube is Chapter 1 of the Class 8 Maths book Ganita Prakash. It is about square numbers and cube numbers. Students learn the patterns in squares and cubes, find square roots and cube roots by different methods, and use them to solve problems.
This page gives 12 important questions from Class 8 Maths Chapter 1 A Square and A Cube with step-by-step answers prepared by Extramarks experts. The questions cover square numbers, cube numbers, square roots and cube roots by prime factorisation, and word problems on square and cube arrangements. Solve each question on paper first and then check your working with the answer.
Q1. Find the square root of 5929 by prime factorization method.
Answer:
Q2. Check whether 15376 is a perfect square using prime factorization.
Answer:
Since all prime factors appear in even powers, 15376 is a perfect square.
Q3. Find the smallest number by which 2352 must be multiplied to make it a perfect square.
Answer:
For a perfect square, we need 3 to appear in an even power. Therefore, multiply by 3.
Q4. Find the square of 47 using the identity
Answer:
Q5. Explain the process to find the smallest number by which 675 must be divided to get a perfect square. Use prime factorization to support your explanation and state the final number.
Answer:
The smallest number by which 675 must be divided so that the quotient is a perfect square is 3.
Q6. A packaging company manufactures identical cubic gift boxes. They receive an order for 13,824 boxes, and they arrange them in a large perfect cube-shaped stack for storage in their warehouse.
The following information is known: Each gift box has a side length of 12 cm. All 13,824 boxes are arranged to form the largest possible cube, which uses all boxes. For shipping, the company wants to pack the entire cubic stack into a larger wooden cubical container, leaving 3 cm of free space on all sides.
Using the above information, answer the following questions.
(i) How many boxes are placed along one edge of the cubic stack?
(ii) What is the side length of the entire cubic stack? (in cm)
(iii) What should be the inner side length of the wooden cube container if there must be 3 cm of empty space on each of the six faces?
(iv) If the wooden container’s thickness is 2 cm on each side, find its outer side length.
Answer: (i) Boxes per edge:
So, the stack has 24 boxes along each edge.
(ii) Side length of the entire cubic stack: each box side = 12 cm
So, the stack measures 288 cm on each side.
(iii) Inner side length of the wooden container: 3 cm free space on each side adds to the length.
Thus,
(iv) Outer side length of the wooden container:
Thus,
Q7. In a school math fair, students design a cube number puzzle. Each clue describes a cube number, but the values include fractions and decimals. You must decode the clues to find the correct numbers.
(b) “If my cube is 0.027, what is my number?”
Answer: a) Let the number be x.
Q8. Check whether 1080 is a perfect cube or not. If not, then what number must be multiplied by it to make it a perfect cube?
Answer:
Q9. There are 800 participants for a yoga practice. The yoga trainer wants to arrange the participants in such a way that the number of participants in each row and the number of rows should be equal. In doing this arrangement, 16 participants are left behind. Explain the complete process to determine the number of rows and the number of participants in each row.
Answer: To arrange 800 participants with 16 left behind, we need to arrange 784 participants (800 – 16) in a square formation where rows equal columns. This means finding n where n² = 784. Calculating the square root: √784 = 28. Therefore, the trainer should arrange participants in 28 rows with 28 participants in each row (28 × 28 = 784), leaving 16 participants behind. This works because 784 is the largest perfect square less than 800.
Q10. A school has 1800 students. The physical education instructor at the school is considering arranging the students in a manner that forms a square of some particular number of students. Based on the provided details, answer the following questions:
(i) Can the physical education instructor form a square with all the students?
(ii) If it is not possible to arrange all the students in a square, find the minimum number of students that need to be excluded from the session to form a square.
(iii) How many more students should be added so that the instructor can form a square?
Answer:
Q11. In a rural plantation program, the agriculture department aims to plant a total of 61009 trees in an organized manner, ensuring that the number of trees in each row is equal to the number of rows. Calculate the total number of rows in the plantation.
Answer:
Q12. Isha is a skilled woodworker, and she's currently working on restoring a square tabletop. As part of her restoration project, she plans to add decorative moldings along the outer edges. Can you calculate the total length of decorative molding she will require to finish the outside edges of the square tabletop?
Answer:
Since length is positive, each side length of the table top is 6 feet.
Related Study Material on Extramarks
- Important Questions Class 8 Maths Chapter 2 Power Play
- Important Questions Class 8 Maths Chapter 3 A Story of Numbers
- Important Questions Class 8 Maths Chapter 4 Quadrilaterals
- Important Questions Class 8 Maths Chapter 5 Number Play
- Important Questions Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply
- Important Questions Class 8 Maths Chapter 7 Proportional Reasoning-1
- Important Questions Class 8 Maths Part 2 Chapter 1 Fractions in Disguise
- Important Questions Class 8 Maths Part 2 Chapter 2 The Baudhayana-Pythagoras Theorem
- Important Questions Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2
- Important Questions Class 8 Maths Part 2 Chapter 4 Exploring Some Geometric Themes
- Important Questions Class 8 Maths Part 2 Chapter 5 Tales by Dots and Lines
- Important Questions Class 8 Maths Part 2 Chapter 6 Algebra Play
- Important Questions Class 8 Maths Part 2 Chapter 7 Area
Q.1
A.
B.
C.
Marks:1
Ans
Q.2 Using the distributive property, find
Marks:1
Ans
Using the distributive property, we have
Hence, the required value is
.
CBSE Class 8 Maths Important Questions
FAQs (Frequently Asked Questions)
Class 8 Maths Chapter 1 is A Square and A Cube. It covers square numbers, cube numbers, square roots, cube roots and number patterns.
Students can check the units digit and prime factorisation. A perfect square cannot end in 2, 3, 7 or 8, and its prime factors must form pairs.
Students can check prime factorisation. A number is a perfect cube when all prime factors can be arranged in triplets.
Only square-numbered lockers remain open because square numbers have an odd number of factors. Other numbers have factors in pairs, so they are toggled an even number of times.
1729 is important because it is the first taxicab number. It can be written as (1^3 + 12^3) and (9^3 + 10^3).