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\ 06-Jan-2025 Bharat Arora Proof-6 Reader’s Sign _______________________ Date __________

Practice Time 6A

1. Find the cube of the following numbers.
(a) 13 (b) 66 (c) –15 (d) 5.8

3 5
(e) –10.1 (f) (g) –
14 11
2. In the following, check whether the given numbers are perfect cubes or not.
(a) 343 (b) 625 (c) 1728 (d) 2744

(e) 6589 (f) 91125 (g) 27000
3. In the following, identify the numbers whose cubes are even numbers.

(a) 122 (b) 525 (c) 728 (d) 2300
(e) 6589 (f) 1123 (g) 9000
4. In the following, identify the numbers whose cubes are odd numbers.
(a) 55 (b) 520 (c) 1227 (d) 2748

(e) 9813 (f) 8125 (g) 10001
5. Give two examples to show that the cube of an even number is always even.

6. Give two examples to show that the cube of an odd number is always odd.
7. Using the prime factorisation method, find which of the following numbers are perfect cubes.
Also, find the number whose perfect cube is the given number.
(a) 432 (b) 625 (c) 2197 (d) 5832
(e) 8000 (f) 10648
8. Find the smallest number by which the given numbers must be multiplied so that the product
becomes a perfect cube.
(a) 72 (b) 128 (c) 576 (d) 392

9. Find the smallest number by which the given numbers must be divided so that it becomes a
perfect cube.

(a) 625 (b) 686 (c) 6750 (d) 5324
3
10. Observe the following pattern: 2 – 1 = 1 + 3 (2 × 1)
3
3
3
3 – 2 = 1 + 3 (3 × 2)
3
3
4 – 3 = 1 + 3 (4 × 3)
Using this pattern, find the value of each of the following:
3
(a) 80 – 79 3 (b) 101 – 100 3
3
Cube Roots

We know that if a cube has a volume of 27 cubic cm. then its each side is of length 3 cm.
Here, 3 = 27. So, 27 is called the cube of 3. Inversely, 3 is the cube root of 27.
3
Thus, the cube root of a number is the value which, when multiplied by itself three times equals
to the original number. The symbol for cube root is 3 .

155 Cubes and Cube Roots