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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 243 · 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 20²? =
  2. 2.A square garden has an area of 1521 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 3364 square m. How long is each side (in m)?
  4. 4.What is √961? =
  5. 5.What is √841? =
  6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 169 (b) 175 (c) 186
  8. 8.What is the smallest whole number by which 126 must be divided to get a perfect square?
  9. 9.What is 29²? =
  10. 10.Which of these is a perfect square? (a) 484 (b) 513 (c) 488
  11. 11.What is the smallest whole number by which 325 must be divided to get a perfect square?
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √8836? =
  14. 14.What is 33²? =
  15. 15.How many whole numbers lie between 27² and 28²?
  16. 16.What is 31²? =
  17. 17.How many whole numbers lie between 23² and 24²?
  18. 18.What is √8649? =
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √729? =
  21. 21.What is 47²? =
  22. 22.Which of these is a perfect square? (a) 560 (b) 529 (c) 568
  23. 23.A square garden has an area of 25 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  25. 25.How many whole numbers lie between 49² and 50²?
  26. 26.A square garden has an area of 1024 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 225 (b) 253 (c) 255
  28. 28.What is the smallest whole number by which 99 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 7² and 8²?
  30. 30.What is √144? =
  31. 31.A square garden has an area of 961 square m. How long is each side (in m)?
  32. 32.What is √5776? =
  33. 33.What is √3481? =
  34. 34.Which of these is a perfect square? (a) 105 (b) 114 (c) 100
  35. 35.A square garden has an area of 121 square m. How long is each side (in m)?
  36. 36.What is √7569? =
  37. 37.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  38. 38.What is the smallest whole number by which 396 must be divided to get a perfect square?
  39. 39.A square garden has an area of 1444 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 35² and 36²?

Answer key

  1. 400
  2. 39
  3. 58
  4. 31
  5. 29
  6. 225
  7. 169
  8. 14
  9. 841
  10. 484
  11. 13
  12. 25
  13. 94
  14. 1089
  15. 54
  16. 961
  17. 46
  18. 93
  19. 625
  20. 27
  21. 2209
  22. 529
  23. 5
  24. 6
  25. 98
  26. 32
  27. 225
  28. 11
  29. 14
  30. 12
  31. 31
  32. 76
  33. 59
  34. 100
  35. 11
  36. 87
  37. 13
  38. 11
  39. 38
  40. 70

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