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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 366 · 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.How many whole numbers lie between 30² and 31²?
  2. 2.What is the smallest whole number by which 375 must be divided to get a perfect square?
  3. 3.What is the smallest whole number by which 98 must be divided to get a perfect square?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 88²? =
  6. 6.How many whole numbers lie between 29² and 30²?
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 272 (b) 256 (c) 257
  9. 9.What is √2601? =
  10. 10.What is √2209? =
  11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √169? =
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √7921? =
  15. 15.What is 54²? =
  16. 16.Which of these is a perfect square? (a) 676 (b) 680 (c) 701
  17. 17.What is 69²? =
  18. 18.What is √7744? =
  19. 19.How many whole numbers lie between 5² and 6²?
  20. 20.What is 67²? =
  21. 21.What is 43²? =
  22. 22.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 99 must be divided to get a perfect square?
  24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 8² and 9²?
  26. 26.A square garden has an area of 3025 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 1165 (b) 1162 (c) 1156
  29. 29.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  30. 30.What is the smallest whole number by which 192 must be divided to get a perfect square?
  31. 31.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  34. 34.How many whole numbers lie between 26² and 27²?
  35. 35.How many whole numbers lie between 13² and 14²?
  36. 36.A square garden has an area of 100 square m. How long is each side (in m)?
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √8281? =
  39. 39.Which of these is a perfect square? (a) 546 (b) 529 (c) 561
  40. 40.How many whole numbers lie between 49² and 50²?

Answer key

  1. 60
  2. 15
  3. 2
  4. 121
  5. 7744
  6. 58
  7. 900
  8. 256
  9. 51
  10. 47
  11. 64
  12. 13
  13. 81
  14. 89
  15. 2916
  16. 676
  17. 4761
  18. 88
  19. 10
  20. 4489
  21. 1849
  22. 5
  23. 11
  24. 441
  25. 16
  26. 55
  27. 49
  28. 1156
  29. 3
  30. 3
  31. 676
  32. 6
  33. 15
  34. 52
  35. 26
  36. 10
  37. 144
  38. 91
  39. 529
  40. 98

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