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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 635 · 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 50 must be multiplied to get a perfect square?
  2. 2.What is √3136? =
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 484 (b) 512 (c) 509
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 1225 square m. How long is each side (in m)?
  8. 8.How many whole numbers lie between 7² and 8²?
  9. 9.What is √2401? =
  10. 10.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 42² and 43²?
  13. 13.What is √1024? =
  14. 14.What is √4096? =
  15. 15.A square garden has an area of 169 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √8281? =
  19. 19.Which of these is a perfect square? (a) 852 (b) 841 (c) 878
  20. 20.What is √841? =
  21. 21.Which of these is a perfect square? (a) 479 (b) 467 (c) 441
  22. 22.A square garden has an area of 784 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 1156 (b) 1175 (c) 1217
  24. 24.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 1444 (b) 1482 (c) 1445
  26. 26.What is √729? =
  27. 27.How many whole numbers lie between 28² and 29²?
  28. 28.A square garden has an area of 3364 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 18 must be divided to get a perfect square?
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √625? =
  32. 32.How many whole numbers lie between 11² and 12²?
  33. 33.Which of these is a perfect square? (a) 1089 (b) 1092 (c) 1094
  34. 34.Which of these is a perfect square? (a) 400 (b) 414 (c) 440
  35. 35.How many whole numbers lie between 50² and 51²?
  36. 36.A square garden has an area of 676 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 31² and 32²?
  38. 38.What is √1764? =
  39. 39.A square garden has an area of 1089 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 289 square m. How long is each side (in m)?

Answer key

  1. 2
  2. 56
  3. 144
  4. 10
  5. 484
  6. 49
  7. 35
  8. 14
  9. 49
  10. 6
  11. 900
  12. 84
  13. 32
  14. 64
  15. 13
  16. 15
  17. 289
  18. 91
  19. 841
  20. 29
  21. 441
  22. 28
  23. 1156
  24. 10
  25. 1444
  26. 27
  27. 56
  28. 58
  29. 2
  30. 81
  31. 25
  32. 22
  33. 1089
  34. 400
  35. 100
  36. 26
  37. 62
  38. 42
  39. 33
  40. 17

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