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Find the cube roots of 27000 and 10648.
To find cube roots: 27000 = 3 × 3 × 3 × 10 × 10 × 10 = (3×10)³ = 30³ ⇒ √³27000 = 30 10648 = 2 × 2 × 2 × 11 × 11 × 11 = (2×11)³ = 22³ ⇒ √³10648 = 22 So, cube roots are 30 and 22 respectively. Both numbers are perfect cubes. For more NCERT Solutions for Class 8 Mathematics Ganita Prakash ChapteRead more
To find cube roots:
27000 = 3 × 3 × 3 × 10 × 10 × 10 = (3×10)³ = 30³ ⇒ √³27000 = 30
10648 = 2 × 2 × 2 × 11 × 11 × 11 = (2×11)³ = 22³ ⇒ √³10648 = 22
So, cube roots are 30 and 22 respectively. Both numbers are perfect cubes.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessCompute successive differences over levels for perfect cubes until all the differences at a level are the same. What do you notice?
When we calculate differences of perfect cubes, we do: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125 First level: 7, 19, 37, 61 Second level: 12, 18, 24 Third level: 6, 6 The third-level differences are constant. This reveals that perfect cubes follow a third-degree pattern. So, the third successive diRead more
When we calculate differences of perfect cubes, we do:
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125
First level: 7, 19, 37, 61
Second level: 12, 18, 24
Third level: 6, 6
The third-level differences are constant. This reveals that perfect cubes follow a third-degree pattern. So, the third successive differences of cubes are always equal.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessIs 500 a perfect cube?
Let’s factorise 500: 500 = 2² × 5³ For a number to be a cube, all prime factors must appear in triplets. Here, the factor 2 appears only twice, which cannot make a group of three. Therefore, 500 is not a perfect cube, as it cannot be written as the cube of any integer. For more NCERT SolutionRead more
Let’s factorise 500:
500 = 2² × 5³
For a number to be a cube, all prime factors must appear in triplets. Here, the factor 2 appears only twice, which cannot make a group of three. Therefore, 500 is not a perfect cube, as it cannot be written as the cube of any integer.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessLet us check if 3375 is a perfect cube.
To check if 3375 is a cube, we do prime factorisation: 3375 = 3³ × 5³ We can group the factors as (3 × 5)³ = 15³ = 3375. Since the prime factors can be grouped into three equal parts, this confirms that 3375 is a perfect cube. Hence, the cube root of 3375 is 15. For more NCERT Solutions for CRead more
To check if 3375 is a cube, we do prime factorisation:
3375 = 3³ × 5³
We can group the factors as (3 × 5)³ = 15³ = 3375. Since the prime factors can be grouped into three equal parts, this confirms that 3375 is a perfect cube.
Hence, the cube root of 3375 is 15.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See lessThe next two taxicab numbers after 1729 are 4104 and 13832. Find the two ways in which each of these can be expressed as the sum of two positive cubes.
A taxicab number is a number expressible as a sum of two cubes in two ways. For 4104: → 2³ + 16³ = 8 + 4096 = 4104 → 9³ + 15³ = 729 + 3375 = 4104 For 13832: → 2³ + 24³ = 8 + 13824 = 13832 → 18³ + 20³ = 5832 + 8000 = 13832 Hence, both 4104 and 13832 are taxicab numbers. For more NCERT SolutionRead more
A taxicab number is a number expressible as a sum of two cubes in two ways.
For 4104:
→ 2³ + 16³ = 8 + 4096 = 4104
→ 9³ + 15³ = 729 + 3375 = 4104
For 13832:
→ 2³ + 24³ = 8 + 13824 = 13832
→ 18³ + 20³ = 5832 + 8000 = 13832
Hence, both 4104 and 13832 are taxicab numbers.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/
See less