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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 318 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 48² and 49²?
  3. 3.What is √8464? =
  4. 4.What is 63²? =
  5. 5.How many whole numbers lie between 30² and 31²?
  6. 6.What is 32²? =
  7. 7.How many whole numbers lie between 10² and 11²?
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 27² and 28²?
  10. 10.What is √1089? =
  11. 11.What is 33²? =
  12. 12.A square garden has an area of 196 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 121 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 539 (b) 550 (c) 529
  15. 15.Which of these is a perfect square? (a) 1521 (b) 1580 (c) 1538
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 92²? =
  18. 18.How many whole numbers lie between 26² and 27²?
  19. 19.Which of these is a perfect square? (a) 907 (b) 900 (c) 933
  20. 20.What is √1521? =
  21. 21.What is the smallest whole number by which 126 must be divided to get a perfect square?
  22. 22.How many whole numbers lie between 18² and 19²?
  23. 23.Which of these is a perfect square? (a) 400 (b) 433 (c) 408
  24. 24.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √3969? =
  27. 27.What is √361? =
  28. 28.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  29. 29.What is √7744? =
  30. 30.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  31. 31.What is √9604? =
  32. 32.What is √9025? =
  33. 33.How many whole numbers lie between 34² and 35²?
  34. 34.Which of these is a perfect square? (a) 830 (b) 784 (c) 835
  35. 35.Which of these is a perfect square? (a) 676 (b) 681 (c) 683
  36. 36.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 65²? =
  38. 38.A square garden has an area of 441 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 292 (b) 320 (c) 289

Answer key

  1. 625
  2. 96
  3. 92
  4. 3969
  5. 60
  6. 1024
  7. 20
  8. 784
  9. 54
  10. 33
  11. 1089
  12. 14
  13. 11
  14. 529
  15. 1521
  16. 400
  17. 8464
  18. 52
  19. 900
  20. 39
  21. 14
  22. 36
  23. 400
  24. 3
  25. 225
  26. 63
  27. 19
  28. 13
  29. 88
  30. 13
  31. 98
  32. 95
  33. 68
  34. 784
  35. 676
  36. 900
  37. 4225
  38. 21
  39. 13
  40. 289

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