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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 480 · 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 smallest whole number by which 56 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 704 must be divided to get a perfect square?
  3. 3.What is 43²? =
  4. 4.How many whole numbers lie between 33² and 34²?
  5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 247 (b) 225 (c) 239
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 20² and 21²?
  9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 21² and 22²?
  11. 11.How many whole numbers lie between 27² and 28²?
  12. 12.How many whole numbers lie between 5² and 6²?
  13. 13.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  14. 14.What is √3136? =
  15. 15.A square garden has an area of 900 square m. How long is each side (in m)?
  16. 16.What is √1444? =
  17. 17.How many whole numbers lie between 17² and 18²?
  18. 18.What is √6724? =
  19. 19.How many whole numbers lie between 8² and 9²?
  20. 20.A square garden has an area of 625 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 1444 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 441 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 144 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 112 must be divided to get a perfect square?
  25. 25.What is √4900? =
  26. 26.What is 20²? =
  27. 27.What is √784? =
  28. 28.What is √961? =
  29. 29.What is 89²? =
  30. 30.What is √1936? =
  31. 31.What is 21²? =
  32. 32.How many whole numbers lie between 43² and 44²?
  33. 33.What is the smallest whole number by which 32 must be divided to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 1444 (b) 1486 (c) 1489
  35. 35.Which of these is a perfect square? (a) 334 (b) 324 (c) 349
  36. 36.What is 97²? =
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 11²? =
  39. 39.What is 27²? =
  40. 40.What is the smallest whole number by which 1134 must be divided to get a perfect square?

Answer key

  1. 14
  2. 11
  3. 1849
  4. 66
  5. 64
  6. 225
  7. 400
  8. 40
  9. 225
  10. 42
  11. 54
  12. 10
  13. 14
  14. 56
  15. 30
  16. 38
  17. 34
  18. 82
  19. 16
  20. 25
  21. 38
  22. 21
  23. 12
  24. 7
  25. 70
  26. 400
  27. 28
  28. 31
  29. 7921
  30. 44
  31. 441
  32. 86
  33. 2
  34. 1444
  35. 324
  36. 9409
  37. 256
  38. 121
  39. 729
  40. 14

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