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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 263 · 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 the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √3721? =
  3. 3.Which of these is a perfect square? (a) 193 (b) 181 (c) 169
  4. 4.What is 48²? =
  5. 5.What is √6889? =
  6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
  7. 7.What is √225? =
  8. 8.What is √289? =
  9. 9.What is 35²? =
  10. 10.A square garden has an area of 676 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 100 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 555 (b) 529 (c) 540
  13. 13.What is 66²? =
  14. 14.Which of these is a perfect square? (a) 151 (b) 144 (c) 153
  15. 15.Which of these is a perfect square? (a) 681 (b) 709 (c) 676
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 25 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 1849 square m. How long is each side (in m)?
  19. 19.A square garden has an area of 625 square m. How long is each side (in m)?
  20. 20.A square garden has an area of 1600 square m. How long is each side (in m)?
  21. 21.What is 87²? =
  22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  23. 23.Which of these is a perfect square? (a) 886 (b) 841 (c) 845
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 27² and 28²?
  26. 26.How many whole numbers lie between 47² and 48²?
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 1521 (b) 1562 (c) 1594
  29. 29.What is √1089? =
  30. 30.A square garden has an area of 3481 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 35² and 36²?
  32. 32.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  33. 33.What is √9025? =
  34. 34.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  35. 35.How many whole numbers lie between 21² and 22²?
  36. 36.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  37. 37.What is 79²? =
  38. 38.What is √1296? =
  39. 39.What is √3481? =
  40. 40.What is 54²? =

Answer key

  1. 64
  2. 61
  3. 169
  4. 2304
  5. 83
  6. 6
  7. 15
  8. 17
  9. 1225
  10. 26
  11. 10
  12. 529
  13. 4356
  14. 144
  15. 676
  16. 225
  17. 5
  18. 43
  19. 25
  20. 40
  21. 7569
  22. 49
  23. 841
  24. 144
  25. 54
  26. 94
  27. 484
  28. 1521
  29. 33
  30. 59
  31. 70
  32. 3
  33. 95
  34. 13
  35. 42
  36. 11
  37. 6241
  38. 36
  39. 59
  40. 2916

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