Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

Cubes and Cube Roots

Which of the following are perfect cubes?

1. 400 2. 3375 3. 8000 4. 15625

5. 9000 6. 6859 7. 2025 8. 10648

1677 Views

Which 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
(i) We have 216 = 2 x 2 x 2 x 3 x 3 x 3Grouping the prime factors of
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.

815 Views

Consider the following pattern:

Express the following numbers as the sum of odd numbers using the above pattern?

(a) 6³ (b) 8³ (c) 7³

36376 Views

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

	Number	Number ending in	Unit’s digit in the cube
(i)	3331	1	1
(ii)	8888	8	2
(iii)	149	9	9
(iv)	1005	5	5
(v)	1024	4	4
(vi)	77	7	3
(vii)	5022	2	8
(viii)	53	3	7

6102 Views

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?

(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5
We do not get complete triples of prime factors, i.e. 2 x 2 and 5 x 5 are left over.

∴ 2700 is not a perfect cube.
(ii) we have 1600 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5
After grouping id 3's we get 5 x 5 which is ungrouped in triples.
(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 1600 is not a perfect cube.
(iii) We have 64000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5
Since, we get groups of triples.
(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 64000 is a perfect cube.
(iv) We have 900 = 2 x 2 x 3 x 3 x 5 x 5
which are ungrouped in triples.

(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 900 is not a perfect cube.
(v) We have 125000 = 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5
As we get all the prime factors in the group of triples.
(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 125000 is a perfect cube
(vi) we have 36000 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5
While grouping the prime factors of 36000 in triples, we are left over with 2 x 2 and 3 x 3
(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 36000 is not a perfect cube
(vii) We have 21600 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5
While grouping the prime factors of 21600 in triples, we are left with 2 x 2 and 5 x 5.
(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 21600 is not a perfect cube
(viii) we have 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
While grouping the prime factors into triples, we are left over with 2 and 5.

(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

∴ 10000 is not a perfect cube
(ix) we have 27000000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5 x 5 x 5

(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete

Since, all the prime factors of 27000000 appear in groups of triples.
∴ 27000000 is a perfect cube.
(x) We have 1000 = 2 x 2 x 2 x 5 x 5 x 5

(i) We have 2700 = 2 x 2 x 3 x 3 x 3 x 5 x 5We do not get complete