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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 379 · 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 43² and 44²?
  2. 2.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  3. 3.What is √2916? =
  4. 4.A square garden has an area of 361 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 1681 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 405 must be divided to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 841 (b) 846 (c) 858
  8. 8.What is 90²? =
  9. 9.How many whole numbers lie between 49² and 50²?
  10. 10.Which of these is a perfect square? (a) 1524 (b) 1587 (c) 1521
  11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √6084? =
  13. 13.What is the smallest whole number by which 54 must be divided to get a perfect square?
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 705 (b) 676 (c) 689
  16. 16.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 217 (b) 210 (c) 196
  18. 18.What is √3136? =
  19. 19.Which of these is a perfect square? (a) 106 (b) 100 (c) 115
  20. 20.What is the smallest whole number by which 45 must be divided to get a perfect square?
  21. 21.How many whole numbers lie between 32² and 33²?
  22. 22.How many whole numbers lie between 50² and 51²?
  23. 23.What is √144? =
  24. 24.How many whole numbers lie between 42² and 43²?
  25. 25.Which of these is a perfect square? (a) 484 (b) 526 (c) 508
  26. 26.Which of these is a perfect square? (a) 784 (b) 812 (c) 827
  27. 27.A square garden has an area of 625 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 1156 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 225 square m. How long is each side (in m)?
  31. 31.What is 18²? =
  32. 32.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  33. 33.A square garden has an area of 2401 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 17²? =
  36. 36.What is √6889? =
  37. 37.What is the smallest whole number by which 63 must be divided to get a perfect square?
  38. 38.What is the smallest whole number by which 540 must be divided to get a perfect square?
  39. 39.How many whole numbers lie between 48² and 49²?
  40. 40.What is 99²? =

Answer key

  1. 86
  2. 10
  3. 54
  4. 19
  5. 41
  6. 5
  7. 841
  8. 8100
  9. 98
  10. 1521
  11. 729
  12. 78
  13. 6
  14. 64
  15. 676
  16. 15
  17. 196
  18. 56
  19. 100
  20. 5
  21. 64
  22. 100
  23. 12
  24. 84
  25. 484
  26. 784
  27. 25
  28. 121
  29. 34
  30. 15
  31. 324
  32. 100
  33. 49
  34. 841
  35. 289
  36. 83
  37. 7
  38. 15
  39. 96
  40. 9801

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