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Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
Among the given numbers, only 1089 is a perfect square (33² = 1089). The other numbers—2032, 2048 and 1027—are not perfect squares because they don’t have whole number square roots. If you try to factor or estimate their roots, you'll find they lie between squares, proving they’re not perfect squareRead more
Among the given numbers, only 1089 is a perfect square (33² = 1089). The other numbers—2032, 2048 and 1027—are not perfect squares because they don’t have whole number square roots. If you try to factor or estimate their roots, you’ll find they lie between squares, proving they’re not perfect squares. So, the correct answer is: Only 1089 is a perfect square; the rest are not.
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 lessAkhil has a square piece of cloth of area 125 cm2. He wants to know if he can cut out a square handkerchief of side 15 cm. If not, he wants to know the maximum size handkerchief that can be cut out from this piece of cloth with an integer side length.
Akhil cannot cut a 15 cm × 15 cm square from 125 cm² because 15² = 225, which exceeds the cloth’s area. The largest square he can cut must have an area less than or equal to 125. The closest perfect square less than 125 is 121 and √121 = 11. So, the biggest square handkerchief with an integer side tRead more
Akhil cannot cut a 15 cm × 15 cm square from 125 cm² because 15² = 225, which exceeds the cloth’s area. The largest square he can cut must have an area less than or equal to 125. The closest perfect square less than 125 is 121 and √121 = 11. So, the biggest square handkerchief with an integer side that Akhil can cut is 11 cm × 11 cm.
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 lessAribam and Bijou play a game. One says a number and the other replies with its square root. Aribam starts. He says 25 and Bijou quickly responds with 5. Then Bijou says 81 and Aribam answers 9. The game goes on till Aribam says 250. Bijou is not able to answer because 250 is not a perfect square. Aribam asks Bijou if he can at least provide a number that is close to the square root of 250.
Since 250 is not a perfect square, Bijou can estimate the square root. 15² = 225 and 16² = 256. So, √250 must lie between 15 and 16. Since 250 is closer to 256 than to 225, we can estimate that √250 ≈ 15.8 or just say it is slightly less than 16. This approximation is useful when exact roots are notRead more
Since 250 is not a perfect square, Bijou can estimate the square root. 15² = 225 and 16² = 256. So, √250 must lie between 15 and 16. Since 250 is closer to 256 than to 225, we can estimate that √250 ≈ 15.8 or just say it is slightly less than 16. This approximation is useful when exact roots are not available for non-square 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 lessFind whether 1156 and 2800 are perfect squares using prime factorisation.
1156 is a perfect square because its prime factorisation is 2² × 17². All prime factors appear in pairs, so it equals (2 × 17)² = 34². On the other hand, 2800 = 2⁵ × 5² × 7. The factor 2 appears five times and 7 is unpaired, so we cannot group all the factors into pairs. Hence, 2800 is not a perfectRead more
1156 is a perfect square because its prime factorisation is 2² × 17². All prime factors appear in pairs, so it equals (2 × 17)² = 34². On the other hand, 2800 = 2⁵ × 5² × 7. The factor 2 appears five times and 7 is unpaired, so we cannot group all the factors into pairs. Hence, 2800 is not a perfect square, while 1156 is.
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 156 a perfect square?
156 is not a perfect square because its prime factors are 2 × 2 × 3 × 13. Although 2 × 2 can form a pair, 3 and 13 remain unpaired. A perfect square must have all its prime factors in pairs. Since we cannot group all the factors of 156 into equal pairs, it cannot be written as a number multiplied byRead more
156 is not a perfect square because its prime factors are 2 × 2 × 3 × 13. Although 2 × 2 can form a pair, 3 and 13 remain unpaired. A perfect square must have all its prime factors in pairs. Since we cannot group all the factors of 156 into equal pairs, it cannot be written as a number multiplied by itself. Therefore, 156 is not a perfect 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 less