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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 125 · 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 smallest whole number by which 240 must be multiplied to get a perfect square?
  2. 2.How many whole numbers lie between 49² and 50²?
  3. 3.How many whole numbers lie between 33² and 34²?
  4. 4.How many whole numbers lie between 39² and 40²?
  5. 5.What is the smallest whole number by which 325 must be divided to get a perfect square?
  6. 6.How many whole numbers lie between 32² and 33²?
  7. 7.A square garden has an area of 484 square m. How long is each side (in m)?
  8. 8.What is 86²? =
  9. 9.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  10. 10.What is 79²? =
  11. 11.What is 16²? =
  12. 12.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 1475 (b) 1511 (c) 1444
  14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 971 (b) 961 (c) 999
  16. 16.How many whole numbers lie between 7² and 8²?
  17. 17.A square garden has an area of 361 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 1086 (b) 1024 (c) 1044
  19. 19.What is 31²? =
  20. 20.A square garden has an area of 1849 square m. How long is each side (in m)?
  21. 21.What is √8464? =
  22. 22.A square garden has an area of 441 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 10² and 11²?
  25. 25.What is the smallest whole number by which 40 must be divided to get a perfect square?
  26. 26.What is 99²? =
  27. 27.What is √2025? =
  28. 28.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  29. 29.How many whole numbers lie between 36² and 37²?
  30. 30.Which of these is a perfect square? (a) 956 (b) 924 (c) 900
  31. 31.A square garden has an area of 2704 square m. How long is each side (in m)?
  32. 32.What is 37²? =
  33. 33.A square garden has an area of 36 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 27 must be divided to get a perfect square?
  35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 14²? =
  37. 37.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 21² and 22²?
  39. 39.A square garden has an area of 900 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 1369 square m. How long is each side (in m)?

Answer key

  1. 15
  2. 98
  3. 66
  4. 78
  5. 13
  6. 64
  7. 22
  8. 7396
  9. 10
  10. 6241
  11. 256
  12. 11
  13. 1444
  14. 49
  15. 961
  16. 14
  17. 19
  18. 1024
  19. 961
  20. 43
  21. 92
  22. 21
  23. 784
  24. 20
  25. 10
  26. 9801
  27. 45
  28. 11
  29. 72
  30. 900
  31. 52
  32. 1369
  33. 6
  34. 3
  35. 576
  36. 196
  37. 3
  38. 42
  39. 30
  40. 37

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