To find the nth odd number, we use the formula 2n – 1. This means if you want the 5th odd number, it would be 2×5 – 1 = 9. This formula is important because square numbers are formed by the sum of the first n odd numbers. For example, the sum of the first 4 odd numbers (1 + 3 + 5 + 7) equals 16, whiRead more
To find the nth odd number, we use the formula 2n – 1. This means if you want the 5th odd number, it would be 2×5 – 1 = 9. This formula is important because square numbers are formed by the sum of the first n odd numbers. For example, the sum of the first 4 odd numbers (1 + 3 + 5 + 7) equals 16, which is 4².
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
From 1 to 100, the square numbers are 1² to 10², totaling 10 numbers. From 101 to 200, we have 11² = 121 to 14² = 196, totaling 4 square numbers. As numbers increase, the number of square numbers in each 100-block reduces. The largest perfect square below 1000 is 961, which is 31². This shows how sqRead more
From 1 to 100, the square numbers are 1² to 10², totaling 10 numbers. From 101 to 200, we have 11² = 121 to 14² = 196, totaling 4 square numbers. As numbers increase, the number of square numbers in each 100-block reduces. The largest perfect square below 1000 is 961, which is 31². This shows how square numbers grow and spread across number ranges.
For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:
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:
What is the nth odd number?
To find the nth odd number, we use the formula 2n – 1. This means if you want the 5th odd number, it would be 2×5 – 1 = 9. This formula is important because square numbers are formed by the sum of the first n odd numbers. For example, the sum of the first 4 odd numbers (1 + 3 + 5 + 7) equals 16, whiRead more
To find the nth odd number, we use the formula 2n – 1. This means if you want the 5th odd number, it would be 2×5 – 1 = 9. This formula is important because square numbers are formed by the sum of the first n odd numbers. For example, the sum of the first 4 odd numbers (1 + 3 + 5 + 7) equals 16, which is 4².
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 lessHow many square numbers are there between 1 and 100? How many are between 101 and 200? Using the table of squares you filled earlier, enter the values below, tabulating the number of squares in each block of 100. What is the largest square less than 1000?
From 1 to 100, the square numbers are 1² to 10², totaling 10 numbers. From 101 to 200, we have 11² = 121 to 14² = 196, totaling 4 square numbers. As numbers increase, the number of square numbers in each 100-block reduces. The largest perfect square below 1000 is 961, which is 31². This shows how sqRead more
From 1 to 100, the square numbers are 1² to 10², totaling 10 numbers. From 101 to 200, we have 11² = 121 to 14² = 196, totaling 4 square numbers. As numbers increase, the number of square numbers in each 100-block reduces. The largest perfect square below 1000 is 961, which is 31². This shows how square numbers grow and spread across number ranges.
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 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 less