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The 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 lessCan a cube end with exactly two zeroes (00)? Explain.
A number ending with two zeros is divisible by 100. When cubed, the number is multiplied by itself three times. That means 100 × 100 × 100 = 1,000,000, which has six zeros. So, even if a number ends in two zeros, its cube will have more than two. Hence, a cube cannot end in exactly two zeros. It musRead more
A number ending with two zeros is divisible by 100. When cubed, the number is multiplied by itself three times. That means 100 × 100 × 100 = 1,000,000, which has six zeros. So, even if a number ends in two zeros, its cube will have more than two. Hence, a cube cannot end in exactly two zeros. It must end in zero or at least three or more zeros.
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 lessSimilar to squares, can you find the number of cubes with 1 digit, 2 digits and 3 digits? What do you observe?
Cubes with: • 1 digit → 1³ = 1, 2³ = 8 • 2 digits → 3³ = 27 to 4³ = 64 • 3 digits → 5³ = 125 to 9³ = 729 Only a few cubes lie in each range. There are fewer cube numbers than squares in low ranges. For example, there are only 2 cubes below 10 and only 4 or 5 in two-digit range. For more NCERTRead more
Cubes with:
• 1 digit → 1³ = 1, 2³ = 8
• 2 digits → 3³ = 27 to 4³ = 64
• 3 digits → 5³ = 125 to 9³ = 729
Only a few cubes lie in each range. There are fewer cube numbers than squares in low ranges. For example, there are only 2 cubes below 10 and only 4 or 5 in two-digit range.
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 lessWe know that 0, 1, 4, 5, 6, 9 are the only last digits possible for squares. What are the possible last digits of cubes?
Cubes can end with several digits, depending on their base number: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000. So, the possible cube endings are 0, 1, 4, 5, 6, 7, 8, 9. Cubes do not end in 2 or 3. For more NCERT Solutions for Class 8 MathemaRead more
Cubes can end with several digits, depending on their base number:
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000.
So, the possible cube endings are 0, 1, 4, 5, 6, 7, 8, 9.
Cubes do not end in 2 or 3.
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 lessCan you estimate the number of unit cubes in a cube with an edge length of 4 units?
To estimate the number of unit cubes in a 4-unit cube, we calculate the cube of the side length. Volume = 4³ = 4 × 4 × 4 = 64 That means the cube is made up of 64 small cubes, each of 1 unit³. Each layer has 4 × 4 = 16 cubes and there are 4 such layers. So, the total number of unit cubes = 64.Read more
To estimate the number of unit cubes in a 4-unit cube, we calculate the cube of the side length.
Volume = 4³ = 4 × 4 × 4 = 64
That means the cube is made up of 64 small cubes, each of 1 unit³.
Each layer has 4 × 4 = 16 cubes and there are 4 such layers.
So, the total number of unit cubes = 64.
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