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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 16 · 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 √2209? =
  2. 2.Which of these is a perfect square? (a) 275 (b) 256 (c) 262
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 32²? =
  5. 5.How many whole numbers lie between 19² and 20²?
  6. 6.Which of these is a perfect square? (a) 324 (b) 343 (c) 334
  7. 7.What is 72²? =
  8. 8.Which of these is a perfect square? (a) 1299 (b) 1308 (c) 1296
  9. 9.What is √7921? =
  10. 10.Which of these is a perfect square? (a) 1149 (b) 1089 (c) 1135
  11. 11.A square garden has an area of 1024 square m. How long is each side (in m)?
  12. 12.What is 49²? =
  13. 13.A square garden has an area of 576 square m. How long is each side (in m)?
  14. 14.How many whole numbers lie between 34² and 35²?
  15. 15.What is √7056? =
  16. 16.What is the smallest whole number by which 72 must be divided to get a perfect square?
  17. 17.What is √484? =
  18. 18.What is the smallest whole number by which 99 must be divided to get a perfect square?
  19. 19.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  20. 20.What is √4489? =
  21. 21.What is √6561? =
  22. 22.What is the smallest whole number by which 250 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 42² and 43²?
  24. 24.How many whole numbers lie between 27² and 28²?
  25. 25.How many whole numbers lie between 10² and 11²?
  26. 26.What is the smallest whole number by which 52 must be divided to get a perfect square?
  27. 27.What is 52²? =
  28. 28.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  29. 29.What is 84²? =
  30. 30.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 126 must be divided to get a perfect square?
  32. 32.What is 89²? =
  33. 33.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  34. 34.What is 99²? =
  35. 35.How many whole numbers lie between 26² and 27²?
  36. 36.Which of these is a perfect square? (a) 1231 (b) 1225 (c) 1286
  37. 37.What is 79²? =
  38. 38.A square garden has an area of 2704 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 256 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 891 must be divided to get a perfect square?

Answer key

  1. 47
  2. 256
  3. 784
  4. 1024
  5. 38
  6. 324
  7. 5184
  8. 1296
  9. 89
  10. 1089
  11. 32
  12. 2401
  13. 24
  14. 68
  15. 84
  16. 2
  17. 22
  18. 11
  19. 3
  20. 67
  21. 81
  22. 10
  23. 84
  24. 54
  25. 20
  26. 13
  27. 2704
  28. 13
  29. 7056
  30. 169
  31. 14
  32. 7921
  33. 3
  34. 9801
  35. 52
  36. 1225
  37. 6241
  38. 52
  39. 16
  40. 11

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