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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 237 · 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 99²? =
  2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 135 (b) 121 (c) 139
  4. 4.What is √625? =
  5. 5.A square garden has an area of 676 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 1193 (b) 1156 (c) 1165
  8. 8.Which of these is a perfect square? (a) 361 (b) 362 (c) 366
  9. 9.Which of these is a perfect square? (a) 830 (b) 804 (c) 784
  10. 10.A square garden has an area of 256 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 484 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 19² and 20²?
  13. 13.A square garden has an area of 121 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 525 (b) 498 (c) 484
  15. 15.What is √1296? =
  16. 16.A square garden has an area of 2116 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 729 square m. How long is each side (in m)?
  19. 19.What is 28²? =
  20. 20.What is the smallest whole number by which 90 must be divided to get a perfect square?
  21. 21.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 40²? =
  23. 23.What is √1089? =
  24. 24.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  25. 25.What is √529? =
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 15² and 16²?
  28. 28.How many whole numbers lie between 38² and 39²?
  29. 29.What is √2916? =
  30. 30.What is √121? =
  31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  33. 33.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 661 (b) 625 (c) 666
  35. 35.A square garden has an area of 784 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 400 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 49 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 196 square m. How long is each side (in m)?
  39. 39.What is 19²? =
  40. 40.What is √6561? =

Answer key

  1. 9801
  2. 729
  3. 121
  4. 25
  5. 26
  6. 100
  7. 1156
  8. 361
  9. 784
  10. 16
  11. 22
  12. 38
  13. 11
  14. 484
  15. 36
  16. 46
  17. 14
  18. 27
  19. 784
  20. 10
  21. 400
  22. 1600
  23. 33
  24. 14
  25. 23
  26. 625
  27. 30
  28. 76
  29. 54
  30. 11
  31. 361
  32. 6
  33. 7
  34. 625
  35. 28
  36. 20
  37. 7
  38. 14
  39. 361
  40. 81

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