Question 1

Which of the following numbers are not perfect squares?
(i) 2032
(ii) 2048
(iii) 1027
(iv) 1089

Accepted Answer

(i) 2032 is not a perfect square, as a number ending with 2 can not be a perfect square.
(ii) 2048 is not a perfect square, as a number ending with 8 can not be a perfect square.
(iii) 1027 is not a perfect square, as a number ending with 7 can not be a perfect square.
(iv) 1089 ends in 9 at the unit’s place. Hence, it is a perfect square.

Question 2

What patterns do you notice? Share your observations and make conjectures. (Page 4)

Accepted Answer

In the above sequence, we notice that the sum of consecutive odd numbers is a perfect square.
We see that the next perfect square is the sum of the next consecutive odd number.
Observation:
1
2
= 1
2
2
= 1 + 3 = 4
3
2
= 1 + 3 + 5 = 9
4
2
= 1 + 3 + 5 + 7 = 16
5
2
= 16 + 9 = 25
6
2
= 25 + 11 = 36
7
2
= 36 + 13 = 49
.
.
.
.
28
2
= 729 + 55 = 784
29
2
= 784 + 57 = 841
30
2
= 841 + 59 = 900

Question 3

Given 125
2
= 15625, what is the value of 126
2
?
(i) 15625 + 126
(ii) 15625+ 26
2
(iii) 15625 + 253
(iv) 15625 + 251
(v) 15625 + 51
2

Accepted Answer

Here, 126
2
= (125 + 1)
2
= (125)
2
+ 2 × 125 × 1 + (1)
2
[Using identity (a + b)
2
= a
2
+ 2ab + b
2
]
= 15625 + 250 + 1
= 15625 + 251
So, the value of 126
2
is (iv) option, i.e., 15625 + 251.

Question 4

Find more such patterns by observing the numbers and their squares from the table you filled earlier. (Page 5)

Accepted Answer

If a number has a 3 or 9 in the units place, its square will always end in 6.
If a number has a 2 or 8 in the units place, its square will always end in 4.
If a number has a 5 in the units place, its square will always end in 5.

Question 5

If a number contains 3 zeros at the end, how many zeros will its square have at the end? (Page 5)

Accepted Answer

If a number contains 3 zeros at the end, then its square will have 6 zeros at the end.

Source: This question is from A Square and A Cube, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Square and A Cube: Number, Contains, Zeros, End, Square, Page. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Square and A CubeQ1: Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Q2: What patterns do you notice? Share your observations and make conjectures. (Page 4)
Q3: Given 125 2 = 15625, what is the value of 126 2 ? (i) 15625 + 126 (ii) 15625+ 26 2 (iii) 15625 +...
Q4: Find more such patterns by observing the numbers and their squares from the table you filled...
Q6: What do you notice about the number of zeros at the end of a number and the number of zeros at the...
Practice more questions from A Square and A Cube &mdash; Mathematics, Class 8 CBSE

Question 6

What do you notice about the number of zeros at the end of a number and the number of zeros at the end of its square? Will this always happen? Can we say that squares can only have an even number of zeros at the end? (Page 5)

Accepted Answer

We noticed that the number of zeros at the end of its square has doubled.
Yes, it will always happen.
And also, we can say that squares can only have an even number of zeros at the end.

Source: This question is from A Square and A Cube, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Square and A Cube: Notice, Number, Zeros, End, Square, Happen. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Square and A CubeQ1: Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Q2: What patterns do you notice? Share your observations and make conjectures. (Page 4)
Q3: Given 125 2 = 15625, what is the value of 126 2 ? (i) 15625 + 126 (ii) 15625+ 26 2 (iii) 15625 +...
Q4: Find more such patterns by observing the numbers and their squares from the table you filled...
Q7: What can you say about the parity of a number and its square? (Page 5)
Practice more questions from A Square and A Cube &mdash; Mathematics, Class 8 CBSE

Question 7

What can you say about the parity of a number and its square? (Page 5)

Accepted Answer

We say that when a number is multiplied by itself, it is called its square.
Figure It Out (Pages 10-11)

Source: This question is from A Square and A Cube, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Square and A Cube: Say, Parity, Number, Square, Page, A Square and A Cube. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Square and A CubeQ1: Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Q2: What patterns do you notice? Share your observations and make conjectures. (Page 4)
Q3: Given 125 2 = 15625, what is the value of 126 2 ? (i) 15625 + 126 (ii) 15625+ 26 2 (iii) 15625 +...
Q4: Find more such patterns by observing the numbers and their squares from the table you filled...
Q6: What do you notice about the number of zeros at the end of a number and the number of zeros at the...
Practice more questions from A Square and A Cube &mdash; Mathematics, Class 8 CBSE

Question 8

In the following pattern, fill in the missing numbers:
1
2
+ 2
2
+ 2
2
= 3
2
2
2
+ 3
2
+ 6
2
= 7
2
3
2
+ 4
2
+ 12
2
= 13
2
4
2
+ 5
2
+ 20
2
= (__)2
9
2
+ 10
2
+ (__)2 = (__)2

Accepted Answer

1
2
+ 2
2
+ 2
2
= 3
2
2
2
+ 3
2
+ 6
2
= 7
2
3
2
+ 4
2
+ 12
2
= 13
2
4
2
+ 5
2
+ 20
2
= (21)
2
9
2
+ 10
2
+ (90)
2
= (91)
2

Source: This question is from A Square and A Cube, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter A Square and A Cube: Pattern, Fill, Missing, Numbers, A Square and A Cube, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from A Square and A CubeQ1: Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Q2: What patterns do you notice? Share your observations and make conjectures. (Page 4)
Q3: Given 125 2 = 15625, what is the value of 126 2 ? (i) 15625 + 126 (ii) 15625+ 26 2 (iii) 15625 +...
Q4: Find more such patterns by observing the numbers and their squares from the table you filled...
Q6: What do you notice about the number of zeros at the end of a number and the number of zeros at the...
Practice more questions from A Square and A Cube &mdash; Mathematics, Class 8 CBSE

Question 9

How many tiny squares are there in the following picture? Write the prime factorisation of the number of tiny squares.

Accepted Answer

Big squares in a row = 9
Big squares in a column = 9
Tiny squares in a big square = 25
∴ Total tiny squares = 9 × 9 × 25 = 2025
Now prime factorisation of 2025 = 3 × 3 × 3 × 3 × 5 × 5 = 452
Figure It Out (Pages 16-17)