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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 568 · 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 √121? =
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 42² and 43²?
  6. 6.How many whole numbers lie between 41² and 42²?
  7. 7.What is the smallest whole number by which 245 must be divided to get a perfect square?
  8. 8.A square garden has an area of 1444 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 24² and 25²?
  10. 10.Which of these is a perfect square? (a) 131 (b) 121 (c) 137
  11. 11.What is √8464? =
  12. 12.Which of these is a perfect square? (a) 398 (b) 361 (c) 365
  13. 13.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 496 (b) 484 (c) 489
  15. 15.Which of these is a perfect square? (a) 239 (b) 231 (c) 225
  16. 16.Which of these is a perfect square? (a) 400 (b) 418 (c) 440
  17. 17.What is the smallest whole number by which 250 must be divided to get a perfect square?
  18. 18.What is √3721? =
  19. 19.How many whole numbers lie between 26² and 27²?
  20. 20.How many whole numbers lie between 21² and 22²?
  21. 21.What is √8649? =
  22. 22.What is the smallest whole number by which 243 must be divided to get a perfect square?
  23. 23.What is 28²? =
  24. 24.Which of these is a perfect square? (a) 609 (b) 583 (c) 576
  25. 25.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 1296 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  31. 31.A square garden has an area of 3249 square m. How long is each side (in m)?
  32. 32.What is 95²? =
  33. 33.What is √196? =
  34. 34.What is 71²? =
  35. 35.Which of these is a perfect square? (a) 1354 (b) 1296 (c) 1367
  36. 36.What is √9801? =
  37. 37.Which of these is a perfect square? (a) 784 (b) 798 (c) 813
  38. 38.A square garden has an area of 81 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 855 (b) 841 (c) 895
  40. 40.What is 49²? =

Answer key

  1. 11
  2. 196
  3. 324
  4. 121
  5. 84
  6. 82
  7. 5
  8. 38
  9. 48
  10. 121
  11. 92
  12. 361
  13. 7
  14. 484
  15. 225
  16. 400
  17. 10
  18. 61
  19. 52
  20. 42
  21. 93
  22. 3
  23. 784
  24. 576
  25. 6
  26. 841
  27. 144
  28. 25
  29. 36
  30. 15
  31. 57
  32. 9025
  33. 14
  34. 5041
  35. 1296
  36. 99
  37. 784
  38. 9
  39. 841
  40. 2401

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