We can guess these cube roots: 1331 = 11³ (last digit is 1) 4913 = 17³ 12167 = 23³ 32768 = 32³ By knowing cube values or estimating from digit patterns, we match these cubes to their roots. For instance, 32³ = 32768, so cube root is 32. This helps in quick identification without full factorisation.Read more
We can guess these cube roots:
1331 = 11³ (last digit is 1)
4913 = 17³
12167 = 23³
32768 = 32³
By knowing cube values or estimating from digit patterns, we match these cubes to their roots. For instance, 32³ = 32768, so cube root is 32. This helps in quick identification without full factorisation.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
1323 = 3³ × 7². For it to be a perfect cube, each prime must occur in multiples of 3. We already have 7², so we need one more 7 to make it 7³. Therefore, multiply 1323 by 7 to get 3³ × 7³ = (3×7)³ = 21³ = 9261 Answer: Multiply by 7 and cube root of the result is 21. For more NCERT Solutions fRead more
1323 = 3³ × 7². For it to be a perfect cube, each prime must occur in multiples of 3.
We already have 7², so we need one more 7 to make it 7³.
Therefore, multiply 1323 by 7 to get 3³ × 7³ = (3×7)³ = 21³ = 9261
Answer: Multiply by 7 and cube root of the result is 21.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
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:
You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Similarly, guess the cube roots of 4913, 12167 and 32768.
We can guess these cube roots: 1331 = 11³ (last digit is 1) 4913 = 17³ 12167 = 23³ 32768 = 32³ By knowing cube values or estimating from digit patterns, we match these cubes to their roots. For instance, 32³ = 32768, so cube root is 32. This helps in quick identification without full factorisation.Read more
We can guess these cube roots:
1331 = 11³ (last digit is 1)
4913 = 17³
12167 = 23³
32768 = 32³
By knowing cube values or estimating from digit patterns, we match these cubes to their roots. For instance, 32³ = 32768, so cube root is 32. This helps in quick identification without full factorisation.
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 lessState true or false. Explain your reasoning. (i) The cube of any odd number is even. (ii) There is no perfect cube that ends with 8. (iii) The cube of a 2-digit number may be a 3-digit number. (iv) The cube of a 2-digit number may have seven or more digits. (v) Cube numbers have an odd number of factors.
(i) False – Odd³ = Odd (e.g., 3³ = 27) (ii) False – 2³ = 8 ends in 8 (iii) True – 4³ = 64 (2-digit → 2-digit), 5³ = 125 (2-digit → 3-digit) (iv) True – 99³ = 970299 (2-digit cube has 6 digits) (v) False – Only cube numbers that are also squares have odd number of factors. Others have even. FoRead more
(i) False – Odd³ = Odd (e.g., 3³ = 27)
(ii) False – 2³ = 8 ends in 8
(iii) True – 4³ = 64 (2-digit → 2-digit), 5³ = 125 (2-digit → 3-digit)
(iv) True – 99³ = 970299 (2-digit cube has 6 digits)
(v) False – Only cube numbers that are also squares have odd number of factors. Others have even.
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 lessWhat number will you multiply by 1323 to make it a cube number?
1323 = 3³ × 7². For it to be a perfect cube, each prime must occur in multiples of 3. We already have 7², so we need one more 7 to make it 7³. Therefore, multiply 1323 by 7 to get 3³ × 7³ = (3×7)³ = 21³ = 9261 Answer: Multiply by 7 and cube root of the result is 21. For more NCERT Solutions fRead more
1323 = 3³ × 7². For it to be a perfect cube, each prime must occur in multiples of 3.
We already have 7², so we need one more 7 to make it 7³.
Therefore, multiply 1323 by 7 to get 3³ × 7³ = (3×7)³ = 21³ = 9261
Answer: Multiply by 7 and cube root of the result is 21.
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 lessFind 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 less