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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 114 · 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 45² and 46²?
  2. 2.Which of these is a perfect square? (a) 1667 (b) 1626 (c) 1600
  3. 3.Which of these is a perfect square? (a) 211 (b) 196 (c) 214
  4. 4.What is 16²? =
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 7² and 8²?
  7. 7.Which of these is a perfect square? (a) 1039 (b) 1024 (c) 1058
  8. 8.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 1123 (b) 1099 (c) 1089
  11. 11.What is 17²? =
  12. 12.Which of these is a perfect square? (a) 1369 (b) 1373 (c) 1408
  13. 13.What is the smallest whole number by which 176 must be divided to get a perfect square?
  14. 14.What is 35²? =
  15. 15.What is √4624? =
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 92²? =
  18. 18.What is √729? =
  19. 19.Which of these is a perfect square? (a) 380 (b) 361 (c) 363
  20. 20.Which of these is a perfect square? (a) 300 (b) 289 (c) 306
  21. 21.A square garden has an area of 900 square m. How long is each side (in m)?
  22. 22.What is 32²? =
  23. 23.Which of these is a perfect square? (a) 782 (b) 749 (c) 729
  24. 24.How many whole numbers lie between 20² and 21²?
  25. 25.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.A square garden has an area of 1600 square m. How long is each side (in m)?
  28. 28.What is 69²? =
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √361? =
  31. 31.Which of these is a perfect square? (a) 1218 (b) 1216 (c) 1156
  32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 892 (b) 860 (c) 841
  34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 68²? =
  36. 36.Which of these is a perfect square? (a) 436 (b) 427 (c) 400
  37. 37.A square garden has an area of 400 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  39. 39.What is 25²? =
  40. 40.What is 29²? =

Answer key

  1. 90
  2. 1600
  3. 196
  4. 256
  5. 289
  6. 14
  7. 1024
  8. 2
  9. 25
  10. 1089
  11. 289
  12. 1369
  13. 11
  14. 1225
  15. 68
  16. 100
  17. 8464
  18. 27
  19. 361
  20. 289
  21. 30
  22. 1024
  23. 729
  24. 40
  25. 15
  26. 86
  27. 40
  28. 4761
  29. 529
  30. 19
  31. 1156
  32. 64
  33. 841
  34. 625
  35. 4624
  36. 400
  37. 20
  38. 2
  39. 625
  40. 841

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