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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 234 · 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.How many whole numbers lie between 17² and 18²?
  2. 2.A square garden has an area of 484 square m. How long is each side (in m)?
  3. 3.What is the smallest whole number by which 448 must be divided to get a perfect square?
  4. 4.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 729 (b) 762 (c) 730
  6. 6.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  7. 7.A square garden has an area of 3481 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  9. 9.How many whole numbers lie between 27² and 28²?
  10. 10.What is the smallest whole number by which 28 must be divided to get a perfect square?
  11. 11.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 784 square m. How long is each side (in m)?
  13. 13.What is 33²? =
  14. 14.A square garden has an area of 324 square m. How long is each side (in m)?
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 87²? =
  17. 17.How many whole numbers lie between 30² and 31²?
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 676 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 65²? =
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 2601 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 3136 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 250 must be divided to get a perfect square?
  27. 27.A square garden has an area of 289 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √3721? =
  30. 30.How many whole numbers lie between 48² and 49²?
  31. 31.Which of these is a perfect square? (a) 317 (b) 303 (c) 289
  32. 32.What is √4624? =
  33. 33.How many whole numbers lie between 21² and 22²?
  34. 34.What is 16²? =
  35. 35.Which of these is a perfect square? (a) 196 (b) 202 (c) 211
  36. 36.Which of these is a perfect square? (a) 1089 (b) 1153 (c) 1099
  37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 14² and 15²?
  39. 39.What is the smallest whole number by which 275 must be divided to get a perfect square?
  40. 40.How many whole numbers lie between 43² and 44²?

Answer key

  1. 34
  2. 22
  3. 7
  4. 625
  5. 729
  6. 13
  7. 59
  8. 5
  9. 54
  10. 7
  11. 7
  12. 28
  13. 1089
  14. 18
  15. 576
  16. 7569
  17. 60
  18. 225
  19. 26
  20. 3
  21. 441
  22. 4225
  23. 361
  24. 51
  25. 56
  26. 10
  27. 17
  28. 100
  29. 61
  30. 96
  31. 289
  32. 68
  33. 42
  34. 256
  35. 196
  36. 1089
  37. 529
  38. 28
  39. 11
  40. 86

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