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All questions of Cubes & Cube Roots for Class 8 Exam
Which of the following is a perfect cube?- a)441
- b)514
- c)412
- d)343
Correct answer is option 'D'. Can you explain this answer?
Which of the following is a perfect cube?
a)
441
b)
514
c)
412
d)
343
 | Ujwal Mukherjee answered |
The perfect cube:
A perfect cube is a number that can be expressed as the cube of an integer. In other words, it is the result of multiplying an integer by itself twice.
Approach:
To determine which of the given options is a perfect cube, we need to find the cube root of each number and check if it is an integer. If the cube root is an integer, then the number is a perfect cube.
Solution:
Let's analyze each option one by one:
a) 441:
To find the cube root of 441, we need to find a number x such that x * x * x = 441. By checking different numbers, we find that the cube root of 441 is 7. Since the cube root is an integer, 441 is a perfect cube.
b) 514:
To find the cube root of 514, we need to find a number x such that x * x * x = 514. By checking different numbers, we find that the cube root of 514 is not an integer. Therefore, 514 is not a perfect cube.
c) 412:
To find the cube root of 412, we need to find a number x such that x * x * x = 412. By checking different numbers, we find that the cube root of 412 is not an integer. Therefore, 412 is not a perfect cube.
d) 343:
To find the cube root of 343, we need to find a number x such that x * x * x = 343. By checking different numbers, we find that the cube root of 343 is 7. Since the cube root is an integer, 343 is a perfect cube.
Conclusion:
Out of the given options, only 343 is a perfect cube. Therefore, the correct answer is option 'D'.
A perfect cube is a number that can be expressed as the cube of an integer. In other words, it is the result of multiplying an integer by itself twice.
Approach:
To determine which of the given options is a perfect cube, we need to find the cube root of each number and check if it is an integer. If the cube root is an integer, then the number is a perfect cube.
Solution:
Let's analyze each option one by one:
a) 441:
To find the cube root of 441, we need to find a number x such that x * x * x = 441. By checking different numbers, we find that the cube root of 441 is 7. Since the cube root is an integer, 441 is a perfect cube.
b) 514:
To find the cube root of 514, we need to find a number x such that x * x * x = 514. By checking different numbers, we find that the cube root of 514 is not an integer. Therefore, 514 is not a perfect cube.
c) 412:
To find the cube root of 412, we need to find a number x such that x * x * x = 412. By checking different numbers, we find that the cube root of 412 is not an integer. Therefore, 412 is not a perfect cube.
d) 343:
To find the cube root of 343, we need to find a number x such that x * x * x = 343. By checking different numbers, we find that the cube root of 343 is 7. Since the cube root is an integer, 343 is a perfect cube.
Conclusion:
Out of the given options, only 343 is a perfect cube. Therefore, the correct answer is option 'D'.
Find the least number which should be added to 500, in order to make the 500, a perfect cube.- a)128
- b)63
- c)12
- d)229
Correct answer is option 'C'. Can you explain this answer?
Find the least number which should be added to 500, in order to make the 500, a perfect cube.
a)
128
b)
63
c)
12
d)
229
 | Shubham Sharma answered |
500 = 2 × 5 × 5 × 5 = 2 × 53
∴ 12 should be added to make the sum, a perfect cube
∴ 12 should be added to make the sum, a perfect cube
Which is the least number which should be added to 1720,in order to make it a perfect cube?- a)269
- b)8
- c)469
- d)58
Correct answer is option 'B'. Can you explain this answer?
Which is the least number which should be added to 1720,in order to make it a perfect cube?
a)
269
b)
8
c)
469
d)
58
 | Geetika Shah answered |
1720 > 1000 = 103
∴ 113 = 1331, 123 = 1728
∴ 1728 – 1720 = 8 should be added to 1720 to make the sum, a perfect cube.
∴ 113 = 1331, 123 = 1728
∴ 1728 – 1720 = 8 should be added to 1720 to make the sum, a perfect cube.
193 – 93 will have – as its one of the factors - a)19
- b)9
- c)10
- d)None of these.
Correct answer is option 'C'. Can you explain this answer?
193 – 93 will have – as its one of the factors
a)
19
b)
9
c)
10
d)
None of these.
| | Madhurima Ahuja answered |
will have (19 – 9) has one of its factors∴ 10 will be a factor of (193 – 93)
= 0.004213 + 273 will have – as its one of the factors - a)21
- b)27
- c)48
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
213 + 273 will have – as its one of the factors
a)
21
b)
27
c)
48
d)
None of these
| | Advait Desai answered |
213 + 273 has (21 + 27) as its one of the factors
∴ 48 will be a factor of (213 + 273)
∴ 48 will be a factor of (213 + 273)
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