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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 131 · 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.Which of these is a perfect square? (a) 361 (b) 394 (c) 364
  2. 2.What is √121? =
  3. 3.What is √324? =
  4. 4.Which of these is a perfect square? (a) 310 (b) 289 (c) 320
  5. 5.Which of these is a perfect square? (a) 918 (b) 941 (c) 900
  6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 7² and 8²?
  8. 8.What is 69²? =
  9. 9.Which of these is a perfect square? (a) 1357 (b) 1296 (c) 1311
  10. 10.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 878 (b) 841 (c) 883
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 2500 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 29² and 30²?
  17. 17.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √1849? =
  19. 19.What is the smallest whole number by which 72 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 448 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 576 (b) 616 (c) 608
  22. 22.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  23. 23.How many whole numbers lie between 50² and 51²?
  24. 24.Which of these is a perfect square? (a) 1132 (b) 1119 (c) 1089
  25. 25.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 961 square m. How long is each side (in m)?
  27. 27.What is √8649? =
  28. 28.How many whole numbers lie between 47² and 48²?
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 20² and 21²?
  31. 31.What is 74²? =
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is 68²? =
  34. 34.How many whole numbers lie between 5² and 6²?
  35. 35.What is √5329? =
  36. 36.What is √5625? =
  37. 37.Which of these is a perfect square? (a) 663 (b) 625 (c) 630
  38. 38.What is √225? =
  39. 39.What is the smallest whole number by which 896 must be divided to get a perfect square?
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 361
  2. 11
  3. 18
  4. 289
  5. 900
  6. 625
  7. 14
  8. 4761
  9. 1296
  10. 5
  11. 25
  12. 841
  13. 576
  14. 676
  15. 50
  16. 58
  17. 169
  18. 43
  19. 2
  20. 7
  21. 576
  22. 10
  23. 100
  24. 1089
  25. 2
  26. 31
  27. 93
  28. 94
  29. 900
  30. 40
  31. 5476
  32. 324
  33. 4624
  34. 10
  35. 73
  36. 75
  37. 625
  38. 15
  39. 14
  40. 100

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