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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 409 · 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 √225? =
  2. 2.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 1017 (b) 1000 (c) 961
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 36² and 37²?
  6. 6.What is √169? =
  7. 7.Which of these is a perfect square? (a) 331 (b) 324 (c) 351
  8. 8.What is 14²? =
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √3721? =
  11. 11.How many whole numbers lie between 41² and 42²?
  12. 12.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  13. 13.A square garden has an area of 529 square m. How long is each side (in m)?
  14. 14.What is 75²? =
  15. 15.A square garden has an area of 169 square m. How long is each side (in m)?
  16. 16.What is 87²? =
  17. 17.What is √529? =
  18. 18.A square garden has an area of 2401 square m. How long is each side (in m)?
  19. 19.What is √2601? =
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  21. 21.A square garden has an area of 484 square m. How long is each side (in m)?
  22. 22.What is √1681? =
  23. 23.What is 29²? =
  24. 24.What is the smallest whole number by which 108 must be divided to get a perfect square?
  25. 25.What is the smallest whole number by which 27 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 526 (b) 523 (c) 484
  27. 27.What is 42²? =
  28. 28.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 135 must be divided to get a perfect square?
  31. 31.A square garden has an area of 3025 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 289 (b) 305 (c) 290
  33. 33.Which of these is a perfect square? (a) 784 (b) 827 (c) 786
  34. 34.A square garden has an area of 361 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 50² and 51²?
  36. 36.How many whole numbers lie between 17² and 18²?
  37. 37.Which of these is a perfect square? (a) 1099 (b) 1089 (c) 1121
  38. 38.What is 24²? =
  39. 39.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  40. 40.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 15
  2. 14
  3. 961
  4. 121
  5. 72
  6. 13
  7. 324
  8. 196
  9. 144
  10. 61
  11. 82
  12. 3
  13. 23
  14. 5625
  15. 13
  16. 7569
  17. 23
  18. 49
  19. 51
  20. 81
  21. 22
  22. 41
  23. 841
  24. 3
  25. 3
  26. 484
  27. 1764
  28. 900
  29. 676
  30. 15
  31. 55
  32. 289
  33. 784
  34. 19
  35. 100
  36. 34
  37. 1089
  38. 576
  39. 10
  40. 169

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