Question

Cubes and Cube Roots

Test
Maximum marks- 24
Maximum time- 35 minutes
1. Is 343 or 243 a perfect cube? (2)
2. Find the cube root of 8000. (2)
3. Find the cube root of 13824. (2)
4. Is 292 a perfect cube? If not find the smallest natural number by which it must be multiplied so that the product is a perfect cube. (4)
5. Show that 1728 is a perfect cube. (2)
6. What is the number whose cube is 216? (2)
7. Find the smallest number by which 68600 must be multiplied to get a perfect cube. (3)
8. Which smallest natural number should divide 1188 so that the quotient is a perfect cube? (3)
9. Is the cube of 4913 an odd number? Why? (2)
10. Is the cube of 132651 an even number? Why? (2)
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Answer 1

1. 343 is the perfect cube of 7 and 243 is not a perfect cube

2. The cube root of 8000 is 20×20×20

3. The cube root of 13824 is 2×2×2×2×2×2×2×2×2×3×3×3

4. 292 is not a perfect cube

5. The perfect square of 1728 is 2×2×2×2×2×2×3×3×3

6. 216 is the cube root of a 6

7. 5 is the smallest number that must be multiplied to make 68600 a perfect cube.

8. 22 is the smallest number that must be divided to make 1188 a perfect cube

9. Yes,the cube of 4913 is also the odd number because when the unit digit is odd the cube is also the odd

10. No, the cube of 132651 is not in even number but if the unit digit is even so the cube is even but there is the unit digit is odd so the cube is also the odd number

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