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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 537 · 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 81²? =
  2. 2.A square garden has an area of 676 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 22² and 23²?
  4. 4.A square garden has an area of 64 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 1574 (b) 1521 (c) 1582
  6. 6.Which of these is a perfect square? (a) 254 (b) 234 (c) 225
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 529 (b) 535 (c) 544
  12. 12.What is √8464? =
  13. 13.What is √4489? =
  14. 14.What is √5184? =
  15. 15.A square garden has an area of 169 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 841 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √7921? =
  19. 19.A square garden has an area of 1521 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 289 (b) 310 (c) 303
  21. 21.What is 72²? =
  22. 22.How many whole numbers lie between 6² and 7²?
  23. 23.What is 63²? =
  24. 24.What is the smallest whole number by which 486 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 1089 (b) 1105 (c) 1150
  26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 30²? =
  29. 29.What is 33²? =
  30. 30.What is √4356? =
  31. 31.What is 42²? =
  32. 32.What is √2025? =
  33. 33.What is 77²? =
  34. 34.Which of these is a perfect square? (a) 961 (b) 971 (c) 970
  35. 35.What is √169? =
  36. 36.What is 70²? =
  37. 37.Which of these is a perfect square? (a) 274 (b) 269 (c) 256
  38. 38.Which of these is a perfect square? (a) 1024 (b) 1061 (c) 1034
  39. 39.What is √3481? =
  40. 40.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 6561
  2. 26
  3. 44
  4. 8
  5. 1521
  6. 225
  7. 289
  8. 14
  9. 14
  10. 49
  11. 529
  12. 92
  13. 67
  14. 72
  15. 13
  16. 29
  17. 324
  18. 89
  19. 39
  20. 289
  21. 5184
  22. 12
  23. 3969
  24. 6
  25. 1089
  26. 361
  27. 729
  28. 900
  29. 1089
  30. 66
  31. 1764
  32. 45
  33. 5929
  34. 961
  35. 13
  36. 4900
  37. 256
  38. 1024
  39. 59
  40. 576

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