Are these practice questions for A Square and A Cube based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 8 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for A Square and A Cube free?

Yes. Every chapter includes free practice questions for Class 8 students to get you started.

What types of questions are included?

The practice set for A Square and A Cube mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for A Square and A Cube for full coverage.

How many practice questions are there for A Square and A Cube?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

A Square and A Cube Class 8 Mathematics Practice Questions with Answers

easy

What is the value of

5^3

?

Try solving it in your notebook first, then check the solution.

easy

State the property of a perfect square related to the number of zeros at the end.

Try solving it in your notebook first, then check the solution.

easy

Examine the number 7744. Without calculating the square root, determine the units digit of its square root.

Try solving it in your notebook first, then check the solution.

easy

Define a perfect square.

Try solving it in your notebook first, then check the solution.

easy

Calculate the square of

1.5

.

Try solving it in your notebook first, then check the solution.

easy

A square-shaped garden has an area of

729 \text{ m}^2

. Calculate the length of the fence required to enclose the garden completely.

Try solving it in your notebook first, then check the solution.

easy

Identify which of the following numbers cannot be a perfect square, based on its units digit: 144, 169, 197, 225.

Try solving it in your notebook first, then check the solution.

easy

Identify the square of each of the following numbers: (i) 11 (ii) 15 (iii) 20.

Try solving it in your notebook first, then check the solution.

easy

List the possible digits in the units place of a perfect square number.

Try solving it in your notebook first, then check the solution.

easy

Explain why a number ending in the digit 2, 3, 7, or 8 cannot be a perfect square.

Try solving it in your notebook first, then check the solution.

easy

List all the perfect squares that are between 50 and 150.

Try solving it in your notebook first, then check the solution.

easy

Calculate the value of

\sqrt[3]{-1331}

.

Try solving it in your notebook first, then check the solution.

easy

Examine the pattern:

1^2 = 1

,

11^2 = 121

,

111^2 = 12321

. Apply this pattern to find the square of

11111

.

Try solving it in your notebook first, then check the solution.

easy

Propose a number greater than 1 that is both a perfect square and a perfect cube. Justify your choice using prime factorization.

Try solving it in your notebook first, then check the solution.

easy

Justify why a perfect square cannot end in the digit 7, using the concept of the unit digits of numbers from 0 to 9.

Try solving it in your notebook first, then check the solution.

medium

Without performing the full calculation, state the units digit of the square of each of the following numbers: (i) 27 (ii) 109 (iii) 34.

Try solving it in your notebook first, then check the solution.

medium

Critique the statement: "If the sum of the digits of a number is a perfect square, the number itself must be a perfect square." Provide a counterexample to support your critique.

Try solving it in your notebook first, then check the solution.

medium

Explain the term 'cube root'. Then, find the cube root of 216.

Try solving it in your notebook first, then check the solution.

medium

Describe the relationship between perfect squares and the sum of consecutive odd numbers starting from 1. Show with examples for the first four perfect squares.

Try solving it in your notebook first, then check the solution.

medium

Justify algebraically why the sum of the first 'n' odd natural numbers is

n^2

.

Try solving it in your notebook first, then check the solution.

medium

Compare the number of zeros at the end of

800

and its square,

800^2

.

Try solving it in your notebook first, then check the solution.

medium

Calculate the value of

\sqrt{176 + \sqrt{2401}}

.

Try solving it in your notebook first, then check the solution.

medium

Design a 3-step method to find the cube root of a 5-digit perfect cube (e.g., 32768) without using prime factorization. Your method should rely on analyzing the unit digit and the remaining digits.

Try solving it in your notebook first, then check the solution.

medium

Solve for the smallest whole number by which 392 must be multiplied to get a perfect square. Also, calculate the square root of the new number.

Try solving it in your notebook first, then check the solution.

medium

Analyze the number 21952. Use prime factorization to determine if it is a perfect cube. If yes, calculate its cube root.

Try solving it in your notebook first, then check the solution.

medium

Evaluate the claim: "The cube of a two-digit number can never have more than six digits." Justify your conclusion by considering the smallest and largest two-digit numbers.

Try solving it in your notebook first, then check the solution.

medium

Justify why the difference between the squares of two consecutive integers,

(n+1)^2 - n^2

, is always an odd number. Use this property to find

51^2

if you know

50^2 = 2500

.

Try solving it in your notebook first, then check the solution.

medium

Evaluate which method is more efficient for determining if 729 is a perfect square: repeated subtraction of odd numbers or prime factorization. Justify your reasoning.

Try solving it in your notebook first, then check the solution.

medium

Formulate a general rule for the number of non-perfect square integers between two consecutive perfect squares,

n^2

and

(n+1)^2

. Justify your rule.

Try solving it in your notebook first, then check the solution.

medium

The volume of a cubical box is

5832 \text{ cm}^3

. Calculate the length of one edge of the box.

Try solving it in your notebook first, then check the solution.

medium

A general wishes to arrange his 8289 soldiers in the form of a square. After arranging them, he found that 8 soldiers were left out. Calculate how many soldiers were there in each row of the square formation.

Try solving it in your notebook first, then check the solution.

medium

Summarize the prime factorization method used to identify if a number is a perfect cube.

Try solving it in your notebook first, then check the solution.

medium

Describe the method of repeated subtraction to determine if a number is a perfect square. Use this method to find the square root of 49.

Try solving it in your notebook first, then check the solution.

medium

List the cubes of the first 10 natural numbers. From your list, identify and describe the pattern of the units digits of the cubes.

Try solving it in your notebook first, then check the solution.

medium

Explain the difference between a square number and a cube number. Provide two examples of perfect squares, two examples of perfect cubes, and one example of a number that is both a perfect square and a perfect cube.

Try solving it in your notebook first, then check the solution.

medium

A school collected ₹2401 from its students for a charity fund. Each student donated as many rupees as the number of students in the school. Calculate the number of students in the school and the amount donated by each student.

Try solving it in your notebook first, then check the solution.

medium

Apply the property of successive odd numbers to demonstrate that 49 is a perfect square.

Try solving it in your notebook first, then check the solution.

hard

The locker puzzle in the source text results in lockers with square numbers remaining open. Formulate a new rule for the puzzle such that only the lockers with numbers that are perfect cubes (up to 1000) will remain open. Describe the actions of Person 2 and Person 3 under your new rule.

Try solving it in your notebook first, then check the solution.

hard

The sum of two cubes can be factored as

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

. Use this formula to verify that 1729 can be expressed as the sum of two cubes in two different ways (

1^3 + 12^3

and

9^3 + 10^3

). Then, critique why this factorization alone is not sufficient to find such "taxicab" numbers easily.

Try solving it in your notebook first, then check the solution.

hard

Solve for the smallest number that should be subtracted from 1989 to make it a perfect square. Also, calculate the square root of the resulting perfect square.

Try solving it in your notebook first, then check the solution.

hard

Prove that for any natural number

n > 1

, the triplet

(2n, n^2-1, n^2+1)

forms a Pythagorean triplet. Then, create three different Pythagorean triplets using this formula.

Try solving it in your notebook first, then check the solution.

hard

Formulate a hypothesis about the relationship between the number of digits in a number (

d

) and the number of digits in its cube. Test your hypothesis for 1-digit, 2-digit, and 3-digit numbers, and justify your conclusion.

Try solving it in your notebook first, then check the solution.

hard

Three metallic cubes with edges 3 cm, 4 cm, and 5 cm respectively are melted and recast into a single, larger cube. Calculate the edge of the new cube formed.

Try solving it in your notebook first, then check the solution.

hard

Create a problem where one must find the smallest number to multiply 1080 by to make it a perfect square, and then find the smallest number to divide the result by to make it a perfect cube. Solve the problem you have created.

Try solving it in your notebook first, then check the solution.

hard

A general has to arrange his soldiers, numbering 8200, in the form of a solid square. After arranging them, he found that some soldiers were left out. Design a process to calculate how many soldiers were left out. Then, propose the minimum number of additional soldiers required to form the next larger solid square.

Try solving it in your notebook first, then check the solution.

A Square and A CubeClass 8 Mathematics Practice Questions