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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 305 · 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 832 must be multiplied to get a perfect square?
  2. 2.Which of these is a perfect square? (a) 205 (b) 209 (c) 196
  3. 3.How many whole numbers lie between 31² and 32²?
  4. 4.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 8² and 9²?
  6. 6.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √3600? =
  8. 8.Which of these is a perfect square? (a) 1024 (b) 1075 (c) 1034
  9. 9.What is 76²? =
  10. 10.How many whole numbers lie between 36² and 37²?
  11. 11.Which of these is a perfect square? (a) 441 (b) 450 (c) 447
  12. 12.A square garden has an area of 100 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 15² and 16²?
  14. 14.What is the smallest whole number by which 486 must be divided to get a perfect square?
  15. 15.How many whole numbers lie between 24² and 25²?
  16. 16.Which of these is a perfect square? (a) 576 (b) 600 (c) 605
  17. 17.What is √256? =
  18. 18.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  19. 19.What is √1849? =
  20. 20.What is 47²? =
  21. 21.What is 87²? =
  22. 22.What is √1936? =
  23. 23.What is √4356? =
  24. 24.What is √625? =
  25. 25.What is 65²? =
  26. 26.Which of these is a perfect square? (a) 668 (b) 645 (c) 625
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  28. 28.How many whole numbers lie between 43² and 44²?
  29. 29.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  30. 30.What is 51²? =
  31. 31.What is √9801? =
  32. 32.What is 91²? =
  33. 33.What is √324? =
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  35. 35.Which of these is a perfect square? (a) 431 (b) 413 (c) 400
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.Which of these is a perfect square? (a) 148 (b) 152 (c) 144
  38. 38.A square garden has an area of 64 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 27² and 28²?

Answer key

  1. 13
  2. 196
  3. 62
  4. 676
  5. 16
  6. 729
  7. 60
  8. 1024
  9. 5776
  10. 72
  11. 441
  12. 10
  13. 30
  14. 6
  15. 48
  16. 576
  17. 16
  18. 14
  19. 43
  20. 2209
  21. 7569
  22. 44
  23. 66
  24. 25
  25. 4225
  26. 625
  27. 144
  28. 86
  29. 14
  30. 2601
  31. 99
  32. 8281
  33. 18
  34. 25
  35. 400
  36. 49
  37. 144
  38. 8
  39. 15
  40. 54

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