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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 609 · 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 sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  5. 5.What is the smallest whole number by which 18 must be divided to get a perfect square?
  6. 6.What is √361? =
  7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 9² and 10²?
  9. 9.How many whole numbers lie between 49² and 50²?
  10. 10.How many whole numbers lie between 23² and 24²?
  11. 11.A square garden has an area of 784 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 504 must be divided to get a perfect square?
  13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 387 (b) 398 (c) 361
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  18. 18.What is 18²? =
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √529? =
  21. 21.What is 72²? =
  22. 22.What is √2500? =
  23. 23.Which of these is a perfect square? (a) 1039 (b) 1052 (c) 1024
  24. 24.What is 64²? =
  25. 25.What is the smallest whole number by which 250 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 127 (b) 124 (c) 121
  27. 27.Which of these is a perfect square? (a) 100 (b) 105 (c) 114
  28. 28.What is 82²? =
  29. 29.What is √289? =
  30. 30.Which of these is a perfect square? (a) 441 (b) 473 (c) 471
  31. 31.A square garden has an area of 3600 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 16² and 17²?
  33. 33.Which of these is a perfect square? (a) 256 (b) 273 (c) 263
  34. 34.Which of these is a perfect square? (a) 324 (b) 326 (c) 359
  35. 35.What is the smallest whole number by which 180 must be divided to get a perfect square?
  36. 36.How many whole numbers lie between 18² and 19²?
  37. 37.What is the smallest whole number by which 891 must be divided to get a perfect square?
  38. 38.What is √2704? =
  39. 39.How many whole numbers lie between 13² and 14²?
  40. 40.What is 36²? =

Answer key

  1. 49
  2. 10
  3. 784
  4. 2
  5. 2
  6. 19
  7. 676
  8. 18
  9. 98
  10. 46
  11. 28
  12. 14
  13. 324
  14. 361
  15. 256
  16. 225
  17. 3
  18. 324
  19. 81
  20. 23
  21. 5184
  22. 50
  23. 1024
  24. 4096
  25. 10
  26. 121
  27. 100
  28. 6724
  29. 17
  30. 441
  31. 60
  32. 32
  33. 256
  34. 324
  35. 5
  36. 36
  37. 11
  38. 52
  39. 26
  40. 1296

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