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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 525 · 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 34²? =
  2. 2.What is √5329? =
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 214 (b) 199 (c) 196
  5. 5.What is 22²? =
  6. 6.What is √7056? =
  7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 50² and 51²?
  9. 9.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 1444 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 13² and 14²?
  12. 12.How many whole numbers lie between 47² and 48²?
  13. 13.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √225? =
  16. 16.A square garden has an area of 361 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 310 (b) 289 (c) 303
  18. 18.A square garden has an area of 144 square m. How long is each side (in m)?
  19. 19.What is 60²? =
  20. 20.What is 72²? =
  21. 21.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  22. 22.What is the smallest whole number by which 18 must be divided to get a perfect square?
  23. 23.A square garden has an area of 36 square m. How long is each side (in m)?
  24. 24.What is √1600? =
  25. 25.Which of these is a perfect square? (a) 256 (b) 273 (c) 272
  26. 26.What is 24²? =
  27. 27.What is 59²? =
  28. 28.A square garden has an area of 2209 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 576 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 36² and 37²?
  33. 33.What is the smallest whole number by which 486 must be divided to get a perfect square?
  34. 34.What is √2116? =
  35. 35.A square garden has an area of 961 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1107 (b) 1128 (c) 1089
  37. 37.Which of these is a perfect square? (a) 1034 (b) 1054 (c) 1024
  38. 38.How many whole numbers lie between 9² and 10²?
  39. 39.A square garden has an area of 2025 square m. How long is each side (in m)?
  40. 40.What is √1089? =

Answer key

  1. 1156
  2. 73
  3. 25
  4. 196
  5. 484
  6. 84
  7. 324
  8. 100
  9. 10
  10. 38
  11. 26
  12. 94
  13. 169
  14. 676
  15. 15
  16. 19
  17. 289
  18. 12
  19. 3600
  20. 5184
  21. 14
  22. 2
  23. 6
  24. 40
  25. 256
  26. 576
  27. 3481
  28. 47
  29. 24
  30. 64
  31. 529
  32. 72
  33. 6
  34. 46
  35. 31
  36. 1089
  37. 1024
  38. 18
  39. 45
  40. 33

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