There is a pattern where the sum of two consecutive triangular numbers equals a perfect square. Triangular numbers like 1, 3, 6, 10 and 15 when paired successively give squares: 1+3=4, 3+6=9, 6+10=16, 10+15=25. This means the next term would be 15+21 = 36 (6²). This connection reveals how triangularRead more
There is a pattern where the sum of two consecutive triangular numbers equals a perfect square. Triangular numbers like 1, 3, 6, 10 and 15 when paired successively give squares: 1+3=4, 3+6=9, 6+10=16, 10+15=25. This means the next term would be 15+21 = 36 (6²). This connection reveals how triangular and square numbers are related through addition, showing beautiful patterns in number theory.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
To find the side of a square from its area, we take the square root of the area. Given the area is 49 sq. cm, we find √49 = 7. This is because 7 × 7 = 49. Therefore, the length of each side of the square is 7 cm. This method is used whenever we know the area and want to determine the side length ofRead more
To find the side of a square from its area, we take the square root of the area. Given the area is 49 sq. cm, we find √49 = 7. This is because 7 × 7 = 49. Therefore, the length of each side of the square is 7 cm. This method is used whenever we know the area and want to determine the side length of a square.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
To find the square root of 64, we ask which number multiplied by itself gives 64. The answer is 8 because 8 × 8 = 64. Also, (–8) × (–8) = 64, but we usually take the positive root. So, √64 = ±8, but in this case, we consider only the positive value. Thus, the square root of 64 is 8. For moreRead more
To find the square root of 64, we ask which number multiplied by itself gives 64. The answer is 8 because 8 × 8 = 64. Also, (–8) × (–8) = 64, but we usually take the positive root. So, √64 = ±8, but in this case, we consider only the positive value. Thus, the square root of 64 is 8.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
To check if a number is a perfect square, we can use two methods. One is by listing perfect squares (1², 2²… etc.) and checking if the number matches one. The other is prime factorisation—if all factors can be grouped into pairs, then it's a perfect square. To find its square root, take one number fRead more
To check if a number is a perfect square, we can use two methods. One is by listing perfect squares (1², 2²… etc.) and checking if the number matches one. The other is prime factorisation—if all factors can be grouped into pairs, then it’s a perfect square. To find its square root, take one number from each pair and multiply. For example, 576 = (2×2×2×2×3×3), so √576 = 24.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
Yes, 324 is a perfect square. When we factorise 324, we get 2 × 2 × 3 × 3 × 3 × 3. These factors can be grouped as (2×3×3) × (2×3×3) = 18 × 18. Since all prime factors are in pairs, it confirms that 324 is a perfect square. Thus, √324 = 18. We use this factor pairing method to confirm perfect squareRead more
Yes, 324 is a perfect square. When we factorise 324, we get 2 × 2 × 3 × 3 × 3 × 3. These factors can be grouped as (2×3×3) × (2×3×3) = 18 × 18. Since all prime factors are in pairs, it confirms that 324 is a perfect square. Thus, √324 = 18. We use this factor pairing method to confirm perfect squares and find their roots.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
Can you see any relation between triangular numbers and square numbers? Extend the pattern shown and draw the next term.
There is a pattern where the sum of two consecutive triangular numbers equals a perfect square. Triangular numbers like 1, 3, 6, 10 and 15 when paired successively give squares: 1+3=4, 3+6=9, 6+10=16, 10+15=25. This means the next term would be 15+21 = 36 (6²). This connection reveals how triangularRead more
There is a pattern where the sum of two consecutive triangular numbers equals a perfect square. Triangular numbers like 1, 3, 6, 10 and 15 when paired successively give squares: 1+3=4, 3+6=9, 6+10=16, 10+15=25. This means the next term would be 15+21 = 36 (6²). This connection reveals how triangular and square numbers are related through addition, showing beautiful patterns in number theory.
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 area of a square is 49 sq. cm. What is the length of its side?
To find the side of a square from its area, we take the square root of the area. Given the area is 49 sq. cm, we find √49 = 7. This is because 7 × 7 = 49. Therefore, the length of each side of the square is 7 cm. This method is used whenever we know the area and want to determine the side length ofRead more
To find the side of a square from its area, we take the square root of the area. Given the area is 49 sq. cm, we find √49 = 7. This is because 7 × 7 = 49. Therefore, the length of each side of the square is 7 cm. This method is used whenever we know the area and want to determine the side length of a square.
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 is the square root of 64?
To find the square root of 64, we ask which number multiplied by itself gives 64. The answer is 8 because 8 × 8 = 64. Also, (–8) × (–8) = 64, but we usually take the positive root. So, √64 = ±8, but in this case, we consider only the positive value. Thus, the square root of 64 is 8. For moreRead more
To find the square root of 64, we ask which number multiplied by itself gives 64. The answer is 8 because 8 × 8 = 64. Also, (–8) × (–8) = 64, but we usually take the positive root. So, √64 = ±8, but in this case, we consider only the positive value. Thus, the square root of 64 is 8.
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 lessGiven a number, such as 576 or 327, how do we find out if it is a perfect square? If it is a perfect square, how can we find its square root?
To check if a number is a perfect square, we can use two methods. One is by listing perfect squares (1², 2²… etc.) and checking if the number matches one. The other is prime factorisation—if all factors can be grouped into pairs, then it's a perfect square. To find its square root, take one number fRead more
To check if a number is a perfect square, we can use two methods. One is by listing perfect squares (1², 2²… etc.) and checking if the number matches one. The other is prime factorisation—if all factors can be grouped into pairs, then it’s a perfect square. To find its square root, take one number from each pair and multiply. For example, 576 = (2×2×2×2×3×3), so √576 = 24.
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 324 a perfect square?
Yes, 324 is a perfect square. When we factorise 324, we get 2 × 2 × 3 × 3 × 3 × 3. These factors can be grouped as (2×3×3) × (2×3×3) = 18 × 18. Since all prime factors are in pairs, it confirms that 324 is a perfect square. Thus, √324 = 18. We use this factor pairing method to confirm perfect squareRead more
Yes, 324 is a perfect square. When we factorise 324, we get 2 × 2 × 3 × 3 × 3 × 3. These factors can be grouped as (2×3×3) × (2×3×3) = 18 × 18. Since all prime factors are in pairs, it confirms that 324 is a perfect square. Thus, √324 = 18. We use this factor pairing method to confirm perfect squares and find their roots.
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