Which of the following numbers is a perfect cube?
Here 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 243 = 3 × 3× 3 × 3 × 3
1331 = 11 × 11 × 11
250 = 2 × 5 × 5 × 5
Clearly 1331 is a perfect cube.
What will be the volume of a cube having edge length 12m? (in m^{3})
Volume of cube = (12)^{3} = 1728 m^{3}
What is the smallest number by which 576 is divided that quotient is a perfect cube?
We have
576 = 2 × 2 × 2 × 3 × 2 × 2 × 2 × 3
∴ 576 should be divided by 9, to get a prefect cube.
If, 1^{3} + 2^{3} + 3^{3} = (1 + 2 + 3)^{2}, 1^{3} + 2^{3} + 3^{3} + 4^{3} = (1 + 2 + 3 + 4)^{2}, then, 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + 6^{3} + 7^{3}
= 784.
Observing the pattern 1^{3} + 2^{3} + 3^{3} = (1 + 2 + 3)^{2}, 1^{3} + 2^{3} + 3^{3} + 4^{3} = (1 + 2 + 3 + 4)^{2} , Find the sum:
1^{3} + 2^{3} + 3^{3} + …… + 9^{3 }= (1 + 2 + 3 …… + 9)^{2}
⇒ (1^{3} + 3^{3} + 5^{3} + 7^{3} + 9^{3}) + 2^{3} (1^{3} + 2^{3}
+ 3^{3} + 4^{3})
= (45)^{2} = 2025
⇒ x + 2^{3} (1 + 2 + 3 + 4)^{2} = 2025
⇒ x = 2025 – 8 × 100 = 1225
Simplify :
Here 12^{2} + 16^{2} = 400
Simplify :
A natural number is of the form (3n + 2). Its cube will be of the form :
(3n + 2)^{3} = 27n^{3} + 8 + 3 × 3n × 2(3n + 2)
= 27n^{3} + 8 + 18n (3n + 2)
= 27n^{3} + 54n^{2} + 36n + 8
= 3 (9n^{3} + 18n^{2} + 12n + 2) + 2
= 3n + 2
A rational number, p < 1, then,
If, 0 < p < 1,
then, p^{3} < p.
A real number ‘p’ is such that p > 1, then
If, p > 1
then, p – 1 > 0
∴ p^{3} > p
Three numbers are in ratio 2 : 3 : 4 and sum of their cubes is 2673. The sum of these numbers are.
Given (2k)^{3} + (3k)^{3} + (4k)^{3} = 2763
⇒ 99 k^{3} = 2763
⇒ k^{3} = 27
⇒ k = 3
∴ Numbers are 6, 9, 12.
∴ Their sum = 6 + 9 + 12 = 27
= ?
Simplify :
We have
Which of the following is not a perfect cube?
513 is not a perfect cube.
The length of edge of a cube whose volume is 74.088 m^{3}.
4.2m = (74.088m^{3})^{1/3}
What is the smallest number by which 3087 may be multiplied so that the product is a perfect cube?
Here 3087 = 3 × 3 × 7 × 7 × 7 = 3^{2} × 7^{3}.
∴ 3087 has two 3 as its factors, but one 3, is short to make 3087, a perfect cube.
∴ 3 should be multiplied to 3087 to produce a perfect cube.
What is the smallest number by which 8788 must be divided so that the duotient is a perfect cube?
8788 = 2 × 2 × 13 × 13 × 13.
∴ 8788 should be divided by (2 × 2), i.e., 4 to produce quotient as a perfect cube.
What is the smallest number by which 392 may be divided so that the duotient is a perfect cube?
392 = 2 × 2 × 2 × 7 × 7
∴ 392 should be divided by (7 × 7), i.e., 49 to produce quotient, i.e., 8 as a perfect cube.
Which of the following is a cube of odd numbers?
2197 = 13^{3}.
∴ The number, i.e., 2197 is odd.
∴ Its cube root should be odd.
Which of the following is a cube of even numbers?
∴ 1278 is even
∴ Its cube root should be even.
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