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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 523 · 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.A square garden has an area of 2304 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 729 (b) 741 (c) 740
  4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 16²? =
  6. 6.What is 59²? =
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 48²? =
  11. 11.How many whole numbers lie between 5² and 6²?
  12. 12.A square garden has an area of 64 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 19² and 20²?
  14. 14.What is √961? =
  15. 15.How many whole numbers lie between 45² and 46²?
  16. 16.How many whole numbers lie between 48² and 49²?
  17. 17.What is √2601? =
  18. 18.How many whole numbers lie between 10² and 11²?
  19. 19.Which of these is a perfect square? (a) 225 (b) 253 (c) 249
  20. 20.How many whole numbers lie between 24² and 25²?
  21. 21.Which of these is a perfect square? (a) 256 (b) 287 (c) 258
  22. 22.What is 62²? =
  23. 23.A square garden has an area of 289 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 8 must be divided to get a perfect square?
  27. 27.What is 64²? =
  28. 28.What is 33²? =
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 39² and 40²?
  31. 31.What is √6400? =
  32. 32.Which of these is a perfect square? (a) 529 (b) 573 (c) 542
  33. 33.Which of these is a perfect square? (a) 784 (b) 793 (c) 812
  34. 34.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  35. 35.What is the smallest whole number by which 539 must be divided to get a perfect square?
  36. 36.How many whole numbers lie between 36² and 37²?
  37. 37.How many whole numbers lie between 37² and 38²?
  38. 38.Which of these is a perfect square? (a) 955 (b) 931 (c) 900
  39. 39.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  40. 40.What is √361? =

Answer key

  1. 48
  2. 484
  3. 729
  4. 289
  5. 256
  6. 3481
  7. 81
  8. 169
  9. 400
  10. 2304
  11. 10
  12. 8
  13. 38
  14. 31
  15. 90
  16. 96
  17. 51
  18. 20
  19. 225
  20. 48
  21. 256
  22. 3844
  23. 17
  24. 36
  25. 15
  26. 2
  27. 4096
  28. 1089
  29. 529
  30. 78
  31. 80
  32. 529
  33. 784
  34. 11
  35. 11
  36. 72
  37. 74
  38. 900
  39. 2
  40. 19

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