Class 8 Exam > Class 8 Notes > Worksheets with Solutions for Class 8 > Worksheet: A Square and A Cube
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Multiple Choice Questions
Q1: Cube root of the expression 1252(a) 5
(b) 25
(c) 10
(d) 125
Q2: Which of the following is not a perfect square number?
(a) 1156
(b) 4657
(c) 4624
(d) 7056
Q3: Which of these is not a perfect cube but a perfect square of a number
(a) 729
(b) 2197
(c) -1331
(d) 169
Q4: Which of these is a perfect cube
(a) 216
(b) 392
(c) 8640
(d) 243
Q5: √0.09 is
(a) 0.3
(b) 0.03
(c) 0.9
(d) 0.33
Q6: The sum of first n odd natural numbers is
(a) n2
(b) 2n
(c) n2+1
(d) n2−1
Q7: The one’s digit of the cube of 53 is:
(a) 9
(b) 3
(c) 7
(d) 1
Q8: The volume of the cube is 5832m3 , the side is
(a) 18m
(b) 16 m
(c) 28 m
(d) 19m
Q9:A perfect square can never have the following digit in its ones place
(a) 8
(b) 4
(c) 0
(d) 1
Q10: Which of the following expressions is not a perfect cube
(a) 27 x 125 x 64
(b) 1331 x 125 x 8
(c) 15 x 8 x 25 x 9
(d) None of these
True and False
Q1: 648 is not a perfect cube.Q2: 999 is a perfect cube.
Q3: The square of a number is positive, so the cube of that number will also be positive.
Q4: 125×8×27 is a perfect cube.
Q5: For an integer p, p3 is always greater than p2.
Q6: 83 = 5.12
Fill in the blanks
Q1: The square of an even number is _____
Q2: The least number by which 72 be multiplied to make it a perfect cube is __________.
Q3: √4096 is ____
Q4: If 8x3=216, then x ix ____
Q5: The cube of .5 is _____
Q6: There are _________ perfect cubes between 1 and 1000.
Q7: The digit at the ones place of 233 is ____
Q8: The cube of the even natural number is ____
Find the cube roots by prime factorization method
Q1: 15625
Q2: 2744
Q3: 125/2197
Q4: 5832
Q5: 64000
Find the square roots by prime factorization method
Q1: 144
Q2: 3600
Q3: 2025
Q4: 81/256
Q5: 1024
Q6: 3844
Answer the following questions
Q1: Is 256 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Q2: What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 1801
(ii) 856
(iii) 1008001
(iv) 6577525
Q3: Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
Q4: Find the smallest number by which following number must be divided to get a perfect square. Also, find the square root of the perfect square so obtained.
(i)600
(ii)2904
Q5: Find the smallest number by which following number must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.
(i) 1008
(ii) 1280
(iii) 1875
You can access the solutions to this Unit Test here.
The document Worksheet: A Square and A Cube | Worksheets with Solutions for Class 8 is a part of the Class 8 Course Worksheets with Solutions for Class 8.
All you need of Class 8 at this link: Class 8
FAQs on Worksheet: A Square and A Cube - Worksheets with Solutions for Class 8
| 1. What is the difference between a square and a cube in mathematics? |  |
Ans. In mathematics, a square of a number is obtained by multiplying the number by itself (e.g., x² = x × x). A cube, on the other hand, is obtained by multiplying the number by itself twice (e.g., x³ = x × x × x). Thus, while both involve powers, squaring is raising to the power of 2 and cubing is raising to the power of 3.
| 2. How can I find the square root of a number using the prime factorization method? | |
Ans. To find the square root using the prime factorization method, first, factor the number into its prime factors. Then, group the prime factors into pairs. The square root is obtained by taking one factor from each pair. For example, for the number 36, the prime factorization is 2² × 3². The square root is 2 × 3 = 6.
| 3. What is the process to find the cube root by the prime factorization method? | |
Ans. To find the cube root using the prime factorization method, factor the number into its prime factors. Then, group the prime factors into triples. The cube root is obtained by taking one factor from each group of three. For instance, for the number 64, the prime factorization is 2³. The cube root is 2, since 2 is taken from the single group of three.
| 4. How do squares and cubes relate to real-life applications? | |
Ans. Squares and cubes have numerous real-life applications. For instance, the area of a square plot of land can be calculated using square measurements, while the volume of a cube-shaped box is calculated using cubic measurements. These concepts are essential in fields such as architecture, engineering, and landscaping.
| 5. Can you explain why prime factorization is useful for finding square and cube roots? | |
Ans. Prime factorization is useful for finding square and cube roots because it breaks down numbers into their basic building blocks, making it easier to identify pairs or triples of factors. This systematic approach simplifies the process of calculating roots, as it allows for clear visualization of the factors involved in the original number.
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