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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 86 · 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 71²? =
  2. 2.Which of these is a perfect square? (a) 298 (b) 293 (c) 289
  3. 3.How many whole numbers lie between 45² and 46²?
  4. 4.How many whole numbers lie between 19² and 20²?
  5. 5.What is √529? =
  6. 6.What is √121? =
  7. 7.A square garden has an area of 2704 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 142 (b) 121 (c) 126
  9. 9.What is 67²? =
  10. 10.A square garden has an area of 900 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √2401? =
  14. 14.How many whole numbers lie between 41² and 42²?
  15. 15.What is √5329? =
  16. 16.Which of these is a perfect square? (a) 900 (b) 944 (c) 940
  17. 17.What is 15²? =
  18. 18.Which of these is a perfect square? (a) 536 (b) 562 (c) 529
  19. 19.Which of these is a perfect square? (a) 256 (b) 262 (c) 263
  20. 20.A square garden has an area of 3364 square m. How long is each side (in m)?
  21. 21.What is 80²? =
  22. 22.What is 99²? =
  23. 23.What is √8464? =
  24. 24.What is 91²? =
  25. 25.What is √1936? =
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 14²? =
  28. 28.A square garden has an area of 121 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 36 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 1410 (b) 1369 (c) 1426
  31. 31.A square garden has an area of 1444 square m. How long is each side (in m)?
  32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is √7921? =
  34. 34.What is √7225? =
  35. 35.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  36. 36.What is 78²? =
  37. 37.How many whole numbers lie between 16² and 17²?
  38. 38.What is √1681? =
  39. 39.What is the smallest whole number by which 99 must be divided to get a perfect square?
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 5041
  2. 289
  3. 90
  4. 38
  5. 23
  6. 11
  7. 52
  8. 121
  9. 4489
  10. 30
  11. 3
  12. 144
  13. 49
  14. 82
  15. 73
  16. 900
  17. 225
  18. 529
  19. 256
  20. 58
  21. 6400
  22. 9801
  23. 92
  24. 8281
  25. 44
  26. 625
  27. 196
  28. 11
  29. 6
  30. 1369
  31. 38
  32. 36
  33. 89
  34. 85
  35. 10
  36. 6084
  37. 32
  38. 41
  39. 11
  40. 729

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