NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part-3Image shows cube root of 1536
Glide to success with Doorsteptutor material for NSTSE Class-8: fully solved questions with step-by-step explanation- practice your way to success.
Question: 3 Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704
Answer:
(i) 81
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime Factors of
Here, one 3 is left which is not in a triplet.
If we divide 81 by 3, then it will become a perfect cube.
Thus, is a perfect cube.
Hence, 81 divided by 3 to make it a perfect cube.
(ii) 128
2 | 128 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime Factors of
Here, one 2is left which is not in a triplet.
If we divide by 2, then it will become a perfect cube.
Thus, is a perfect cube.
Hence, 128 divided by 2 to make it a perfect cube.
(iii) 135
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime Factors of
Here, one 2 is left which is not in a triplet.
If we divide 135 by 5, then it will become a perfect cube
Thus, is a perfect cube.
Hence, 135 divided by 5 to make it a perfect cube.
(iv) 192
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime Factors of
Here, one 3 is left which is not in a triplet.
If we divide 192 by 3, then it will become a perfect cube
Thus, is a perfect cube.
Hence, 192 divided by 3 to make it a perfect cube.
Question: 4 Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
Answer:
Given numbers
Since, factors of 5 and 2 both are not in group of three.
Therefore, the number must be multiplied by to make it a perfect cube. Hence he needs 20 cuboids.