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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 445 · 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.A square garden has an area of 2601 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 820 (b) 838 (c) 784
  3. 3.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √5329? =
  8. 8.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  9. 9.What is 84²? =
  10. 10.Which of these is a perfect square? (a) 484 (b) 513 (c) 487
  11. 11.Which of these is a perfect square? (a) 1608 (b) 1651 (c) 1600
  12. 12.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 5² and 6²?
  15. 15.What is 80²? =
  16. 16.What is 20²? =
  17. 17.What is 46²? =
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1296 (b) 1305 (c) 1323
  20. 20.Which of these is a perfect square? (a) 850 (b) 841 (c) 846
  21. 21.What is √1089? =
  22. 22.What is √196? =
  23. 23.Which of these is a perfect square? (a) 631 (b) 625 (c) 673
  24. 24.What is the smallest whole number by which 63 must be divided to get a perfect square?
  25. 25.How many whole numbers lie between 45² and 46²?
  26. 26.A square garden has an area of 1444 square m. How long is each side (in m)?
  27. 27.What is 65²? =
  28. 28.What is 53²? =
  29. 29.What is 62²? =
  30. 30.What is the smallest whole number by which 8 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 1154 (b) 1089 (c) 1134
  32. 32.What is 79²? =
  33. 33.What is the smallest whole number by which 117 must be divided to get a perfect square?
  34. 34.What is 97²? =
  35. 35.What is √1156? =
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √1369? =
  38. 38.How many whole numbers lie between 47² and 48²?
  39. 39.What is √625? =
  40. 40.Which of these is a perfect square? (a) 112 (b) 100 (c) 119

Answer key

  1. 51
  2. 784
  3. 2
  4. 121
  5. 196
  6. 169
  7. 73
  8. 15
  9. 7056
  10. 484
  11. 1600
  12. 2
  13. 529
  14. 10
  15. 6400
  16. 400
  17. 2116
  18. 676
  19. 1296
  20. 841
  21. 33
  22. 14
  23. 625
  24. 7
  25. 90
  26. 38
  27. 4225
  28. 2809
  29. 3844
  30. 2
  31. 1089
  32. 6241
  33. 13
  34. 9409
  35. 34
  36. 144
  37. 37
  38. 94
  39. 25
  40. 100

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