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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 630 · 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.Which of these is a perfect square? (a) 694 (b) 676 (c) 685
  2. 2.How many whole numbers lie between 38² and 39²?
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 41² and 42²?
  5. 5.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  6. 6.How many whole numbers lie between 7² and 8²?
  7. 7.Which of these is a perfect square? (a) 129 (b) 127 (c) 121
  8. 8.A square garden has an area of 196 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 1217 (b) 1171 (c) 1156
  10. 10.What is 28²? =
  11. 11.What is the smallest whole number by which 98 must be divided to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 1503 (b) 1517 (c) 1444
  13. 13.How many whole numbers lie between 46² and 47²?
  14. 14.What is √1764? =
  15. 15.What is the smallest whole number by which 75 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1651 (b) 1600 (c) 1633
  18. 18.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  21. 21.What is 95²? =
  22. 22.What is √1936? =
  23. 23.What is √1296? =
  24. 24.What is √1600? =
  25. 25.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 2704 square m. How long is each side (in m)?
  27. 27.What is 52²? =
  28. 28.What is √1681? =
  29. 29.A square garden has an area of 676 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 255 (b) 225 (c) 247
  31. 31.What is √4096? =
  32. 32.A square garden has an area of 2500 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 96²? =
  35. 35.A square garden has an area of 3136 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 891 must be divided to get a perfect square?
  38. 38.How many whole numbers lie between 34² and 35²?
  39. 39.A square garden has an area of 100 square m. How long is each side (in m)?
  40. 40.What is 57²? =

Answer key

  1. 676
  2. 76
  3. 784
  4. 82
  5. 3
  6. 14
  7. 121
  8. 14
  9. 1156
  10. 784
  11. 2
  12. 1444
  13. 92
  14. 42
  15. 3
  16. 2
  17. 1600
  18. 5
  19. 400
  20. 5
  21. 9025
  22. 44
  23. 36
  24. 40
  25. 14
  26. 52
  27. 2704
  28. 41
  29. 26
  30. 225
  31. 64
  32. 50
  33. 64
  34. 9216
  35. 56
  36. 576
  37. 11
  38. 68
  39. 10
  40. 3249

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