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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 59 · 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.How many whole numbers lie between 37² and 38²?
  2. 2.A square garden has an area of 3600 square m. How long is each side (in m)?
  3. 3.What is √1600? =
  4. 4.What is 28²? =
  5. 5.What is 66²? =
  6. 6.What is 91²? =
  7. 7.Which of these is a perfect square? (a) 576 (b) 615 (c) 612
  8. 8.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 2025 square m. How long is each side (in m)?
  10. 10.What is 12²? =
  11. 11.A square garden has an area of 289 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 99 must be divided to get a perfect square?
  14. 14.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  15. 15.What is √3844? =
  16. 16.How many whole numbers lie between 29² and 30²?
  17. 17.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √4356? =
  20. 20.What is √2304? =
  21. 21.Which of these is a perfect square? (a) 1355 (b) 1296 (c) 1314
  22. 22.What is √4761? =
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 68²? =
  25. 25.What is √3136? =
  26. 26.What is the smallest whole number by which 98 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 298 (b) 303 (c) 289
  28. 28.What is √1225? =
  29. 29.What is 57²? =
  30. 30.Which of these is a perfect square? (a) 1089 (b) 1141 (c) 1107
  31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 1521 (b) 1533 (c) 1575
  33. 33.How many whole numbers lie between 41² and 42²?
  34. 34.What is 26²? =
  35. 35.What is √1296? =
  36. 36.What is √2209? =
  37. 37.A square garden has an area of 100 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 1521 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 256 (b) 279 (c) 263
  40. 40.What is the smallest whole number by which 245 must be divided to get a perfect square?

Answer key

  1. 74
  2. 60
  3. 40
  4. 784
  5. 4356
  6. 8281
  7. 576
  8. 729
  9. 45
  10. 144
  11. 17
  12. 81
  13. 11
  14. 6
  15. 62
  16. 58
  17. 441
  18. 225
  19. 66
  20. 48
  21. 1296
  22. 69
  23. 676
  24. 4624
  25. 56
  26. 2
  27. 289
  28. 35
  29. 3249
  30. 1089
  31. 324
  32. 1521
  33. 82
  34. 676
  35. 36
  36. 47
  37. 10
  38. 39
  39. 256
  40. 5

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