Short Answer TypeIs 1372 a perfect cube? If not, find the smallest natural number by which 1372 must be multipled so that the product is a perfect cube.
Find the one’s digit of the cube of each of the following numbers.
(i) 3331 (ii) 8888 (iii) 149 (iv) 1005
(v) 1024 (vi) 77 (vii) 5022 (viii) 53
Consider the following pattern:
(a) 63 (b) 83 (c) 73
Long Answer TypeWhich of the following are perfect cubes?
1. 400 2. 3375 3. 8000 4. 15625
5. 9000 6. 6859 7. 2025 8. 10648
Check which of the following are perfect cubes.
(i) 2700 (ii) 16000 (iii) 64000 (iv) 900
(v) 125000 (vi) 36000 (vii) 21600 (viii) 10000
(ix) 27000000 (x) 1000
What pattern do you observe in these perfect cubes?
Short Answer TypeWhich of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656
(i) We have 216 = 2 x 2 x 2 x 3 x 3 x 3
Grouping the prime factors of 216 into triples, no factor is left over.
∴ 216 is a perfect cube.
(ii) We have 128 = 2 x 2 x 2 x 2 x 2 x 2
∴ 128 is not a perfect cube.
(iii) We have 1000 = 2 x 2 x 2 x 5 x 5 x 5
∴ 1000 is a perfect cube.
(iv) We have 100 = 2 x 2 x 5 x 5
Grouping the prime factors into triples, we do not get any triples.
Factors 2 x 2 and 5 x 5 are not in triples.
∴ 100 is not a perfect cube.
(v) We have 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Grouping the prime factors of 46656 in triples we are not left over with any prime factor.
∴ 46656 is a perfect cube.
Long Answer TypeFind the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100
Short Answer Type
Switch
