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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 589 · 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 √1089? =
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 65²? =
  4. 4.What is √8100? =
  5. 5.What is 17²? =
  6. 6.What is 22²? =
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 30²? =
  9. 9.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  10. 10.What is the smallest whole number by which 112 must be divided to get a perfect square?
  11. 11.A square garden has an area of 289 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √1521? =
  14. 14.What is √3025? =
  15. 15.What is 43²? =
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √2025? =
  18. 18.What is the smallest whole number by which 28 must be divided to get a perfect square?
  19. 19.What is √1156? =
  20. 20.Which of these is a perfect square? (a) 695 (b) 676 (c) 706
  21. 21.What is 56²? =
  22. 22.How many whole numbers lie between 9² and 10²?
  23. 23.What is 84²? =
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √9216? =
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 22² and 23²?
  28. 28.What is 81²? =
  29. 29.A square garden has an area of 81 square m. How long is each side (in m)?
  30. 30.What is 37²? =
  31. 31.How many whole numbers lie between 44² and 45²?
  32. 32.How many whole numbers lie between 18² and 19²?
  33. 33.What is the smallest whole number by which 192 must be divided to get a perfect square?
  34. 34.A square garden has an area of 2704 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 1208 (b) 1156 (c) 1220
  36. 36.Which of these is a perfect square? (a) 289 (b) 295 (c) 310
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 91²? =

Answer key

  1. 33
  2. 784
  3. 4225
  4. 90
  5. 289
  6. 484
  7. 289
  8. 900
  9. 3
  10. 7
  11. 17
  12. 81
  13. 39
  14. 55
  15. 1849
  16. 36
  17. 45
  18. 7
  19. 34
  20. 676
  21. 3136
  22. 18
  23. 7056
  24. 676
  25. 96
  26. 841
  27. 44
  28. 6561
  29. 9
  30. 1369
  31. 88
  32. 36
  33. 3
  34. 52
  35. 1156
  36. 289
  37. 256
  38. 400
  39. 361
  40. 8281

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