Each of our Ganita Prakash Class 8 Worksheet and Class 8 Maths Chapter 1 A Square and A Cube Worksheet with Answers Pdf focuses on conceptual clarity.
Class 8 Maths Chapter 1 A Square and A Cube Worksheet with Answers Pdf
A Square and A Cube Class 8 Maths Worksheet
Class 8 Maths Chapter 1 Worksheet with Answers – Class 8 A Square and A Cube Worksheet
Tick (✓) for the correct option
Question 1.
The total non-square numbers that lie between squares of 30 and 31 are
(a) 59
(b) 60
(c) 61
(d) 62
Question 2.
The number of digits in the square root of 7-digit square number is
(a) 3
(b) 4
(c) 6
(d) 7
Question 3.
If \(\sqrt{11025}\) = 105, then \(\sqrt{1.1025}\) is
(a) 1.05
(b) 10.5
(c) 0.105
(d) 105
Question 4.
Which of the following numbers would not have digit 4 at units place?
(a) 642
(6) 722
(c) 782
(d) 1022
Question 5.
The cube of a number
(a) can be positive or negative
(b) can never be zero
(c) is always positive
(d) is always negative
Question 6.
Which of the following is not a perfect cube?
(a) 1331
(b) 10648
(c) 729
(d) 21600
Question 7.
The volume of the cube of edge 1.6 m is
(a) 2.56 m3
(b) 40.96 m3
(c) 4.096 m3
(d) 5.12 m3
Question 8.
The one’s digit of the cube of 23 is
(a) 6
(6) 7
(c) 3
(d) 9
Question 9.
Which of the following numbers is a perfect cube?
(a) 243
(6) 216
(c) 392
(d) 8640
Assertion Reason Questions
In questions 1-4, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
Question 1.
Assertion (A): Every perfect square has an even number of zeros at the end.
Reason (R) : A number ending with an odd number of zeros cannot be expressed as the product of two identical factors.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
Question 2.
Assertion (A): The square root of 0.04 is 0.2.
Reason (R) : The square root of a decimal number can be obtained by removing the decimal point, finding the square root, and then placing the decimal point in the result so that the number of decimal places is halved.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
Question 3.
Assertion (A): The cube of any even number is even, and the cube of any odd number is odd.
Reason (R) : Multiplying three even or three odd numbers together results in an even or odd product respectively.
(а) Both (A) and (R) are true and (R) is the correct explanation of (A).
(б) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
Question 4.
Assertion (A): If the cube root of a number is irrational, then the number itself must be irrational.
Reason (R) : The cube of any irrational number is always rational.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
Fill in the blanks
1. The sum of first ‘n’ __________________ natural numbers is equal to n2.
2. The square of a multiple of 100 always ends in __________________ number of zeroes.
3. If the sum of squares of two numbers is equal to the square of a third number, then the three numbers are said to form a __________________.
4. If a number is multiplied by itself we get its __________________.
5. If a perfect square number ends in 4 its square root will end in __________________ or __________________.
6. If n is a non zero integer, then n × n × n written as __________________ is called __________________ of n.
7. A perfect cube can also be called a perfect __________________.
8 In the prime factorization of any number if each factor appears three times then the number is __________________ cube.
9. Cube of 13 is __________________.
10. Cube of __________________ is -27.
Write (T) for true or (F) for false for the given statements
1. If a number ends in 4, then its square root also ends in 4.
2. The square root of number can never be negative.
3. For two consecutive numbers, difference of the squares is equal to twice the smaller number.
4. There does not exist any perfect square between 50 and 60.
5. A perfect square cannot be odd.
6. If units digit of a number is 2, units digit of its cube is 8.
7. If ‘n’ is a natural number and cube of n is less than 1000, then n – 1, 2, 3, …, 9.
8. If a number ends in two zeros, its cube will end in six zeros.
9. If a number leaves remainder 2 when divided by 3, its cube also leaves the remainder 2 when divided by 3.
10. Cube of an even number is odd and that of an odd number is even.
Very Short Answer Type Questions
Question 1.
By observing the units digit check if 4622 is a perfect square. Give reason.
Solution:
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Question 2.
Is square root of 2710 even? Why?
Solution:
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Question 3.
What is (are) the units digit(s) of the square root of the following perfect squares:
(a) 17424
(b) 23409
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Question 4.
Find the least whole number by which 468 be multiplied to make it a perfect square. Find also the square root of the resulting number.
Solution:
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Question 5.
Find the least whole number by which 8450 be divided to make it a perfect square. Find also the square root of the resulting number.
Solution:
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Question 6.
Find the square root of 961.
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Question 7.
Find the square root of 9,604.
Solution:
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Question 8.
What will be the units digit of the cube of 121?
Solution:
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Question 9.
If 729 is a perfect cube, will 729000000 be a perfect cube? Why?
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Question 10.
Side of a cube is 11 cm. Find its volume.
Solution:
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Question 11.
Square of a number is 25. What will be its cube?
Solution:
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Question 12.
Product of a number and its square is 1000. What is this number?
Solution:
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Question 13.
What will be the units digit of the cube of 532?
Solution:
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Short Answer Type Questions
Question 1.
What least number must be added to 8743 to make it a perfect square?
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Question 2.
Find the greatest number of three digits which is a perfect square.
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Question 3.
Find the length of side of a square whose area is equal to the area of a rectangle whose sides are 64 dm and 25 dm respectively.
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Question 4.
In a square garden the trees are planted in rows. There are as many trees in each row as is the number of rows in the garden. If the total number of trees in the garden is 3025, how many trees are in each row?
Solution:
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Question 5.
A society collected ₹ 9216, each member contributing as many rupees as there were members. Find the number of the members of the society.
Solution:
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Question 6.
If 1331 is a perfect cube, will 133100000 be a perfect cube? Why?
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Question 7.
Find the smallest number by which 3087 be multiplied to make it a perfect cube.
Solution:
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Question 8.
Find the smallest number by which 32928 be multiplied to make it a perfect cube.
Solution:
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Question 9.
By what smallest number should 3600 be multiplied so that the quotient is a perfect cube.
Solution:
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Question 10.
Find the cube root of 10648.
Solution:
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Case-Based Questions
A teacher gave her students four numbers: 729, 1000, 1331, and 800. She asked them to identify which ones are perfect cubes and justify their reasoning. Later, she discussed why certain numbers, though close to cubes, fail to be perfect cubes.
Based on the above information give answers of the following questions:
Question 1.
Which of the given numbers are perfect cubes?
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Question 2.
Explain why 800 is not a perfect cube, even though it lies between 729 and 1000.
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Question 3.
If a number ends with 1, what can you say about its cube root’s unit digit? Justify your answer.
Solution:
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