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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 563 · 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 77²? =
  2. 2.Which of these is a perfect square? (a) 479 (b) 441 (c) 477
  3. 3.What is √1296? =
  4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 3025 square m. How long is each side (in m)?
  7. 7.What is √1521? =
  8. 8.What is the smallest whole number by which 224 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 46² and 47²?
  10. 10.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  11. 11.How many whole numbers lie between 12² and 13²?
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 1089 square m. How long is each side (in m)?
  14. 14.What is √5625? =
  15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 135 (b) 126 (c) 121
  17. 17.Which of these is a perfect square? (a) 100 (b) 105 (c) 120
  18. 18.A square garden has an area of 441 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  20. 20.A square garden has an area of 256 square m. How long is each side (in m)?
  21. 21.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 1521 square m. How long is each side (in m)?
  23. 23.What is 64²? =
  24. 24.What is 47²? =
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 1681 square m. How long is each side (in m)?
  27. 27.What is √4356? =
  28. 28.How many whole numbers lie between 15² and 16²?
  29. 29.What is √2304? =
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  32. 32.What is 40²? =
  33. 33.What is √2916? =
  34. 34.How many whole numbers lie between 44² and 45²?
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 22²? =
  37. 37.What is 70²? =
  38. 38.Which of these is a perfect square? (a) 266 (b) 284 (c) 256
  39. 39.Which of these is a perfect square? (a) 225 (b) 236 (c) 248
  40. 40.What is √2809? =

Answer key

  1. 5929
  2. 441
  3. 36
  4. 729
  5. 676
  6. 55
  7. 39
  8. 14
  9. 92
  10. 3
  11. 24
  12. 100
  13. 33
  14. 75
  15. 441
  16. 121
  17. 100
  18. 21
  19. 14
  20. 16
  21. 225
  22. 39
  23. 4096
  24. 2209
  25. 49
  26. 41
  27. 66
  28. 30
  29. 48
  30. 81
  31. 13
  32. 1600
  33. 54
  34. 88
  35. 289
  36. 484
  37. 4900
  38. 256
  39. 225
  40. 53

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