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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 571 · 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.A square garden has an area of 36 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 1089 square m. How long is each side (in m)?
  3. 3.What is the smallest whole number by which 27 must be divided to get a perfect square?
  4. 4.What is 28²? =
  5. 5.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √1369? =
  7. 7.Which of these is a perfect square? (a) 1093 (b) 1092 (c) 1089
  8. 8.A square garden has an area of 576 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 994 (b) 971 (c) 961
  10. 10.Which of these is a perfect square? (a) 845 (b) 841 (c) 852
  11. 11.What is 31²? =
  12. 12.How many whole numbers lie between 35² and 36²?
  13. 13.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  14. 14.What is 79²? =
  15. 15.What is √1681? =
  16. 16.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  17. 17.What is 24²? =
  18. 18.Which of these is a perfect square? (a) 707 (b) 676 (c) 722
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √1764? =
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √121? =
  23. 23.A square garden has an area of 400 square m. How long is each side (in m)?
  24. 24.What is 21²? =
  25. 25.A square garden has an area of 49 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 47² and 48²?
  27. 27.A square garden has an area of 1936 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 125 must be divided to get a perfect square?
  29. 29.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  30. 30.What is √2025? =
  31. 31.What is 59²? =
  32. 32.Which of these is a perfect square? (a) 324 (b) 342 (c) 335
  33. 33.How many whole numbers lie between 29² and 30²?
  34. 34.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 289 (b) 290 (c) 295
  37. 37.What is 90²? =
  38. 38.What is √5329? =
  39. 39.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  40. 40.What is √1024? =

Answer key

  1. 6
  2. 33
  3. 3
  4. 784
  5. 400
  6. 37
  7. 1089
  8. 24
  9. 961
  10. 841
  11. 961
  12. 70
  13. 3
  14. 6241
  15. 41
  16. 6
  17. 576
  18. 676
  19. 900
  20. 42
  21. 196
  22. 11
  23. 20
  24. 441
  25. 7
  26. 94
  27. 44
  28. 5
  29. 5
  30. 45
  31. 3481
  32. 324
  33. 58
  34. 7
  35. 676
  36. 289
  37. 8100
  38. 73
  39. 10
  40. 32

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