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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 453 · 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 17² and 18²?
  2. 2.Which of these is a perfect square? (a) 240 (b) 226 (c) 225
  3. 3.Which of these is a perfect square? (a) 289 (b) 298 (c) 290
  4. 4.What is √361? =
  5. 5.What is 93²? =
  6. 6.How many whole numbers lie between 15² and 16²?
  7. 7.What is √7396? =
  8. 8.A square garden has an area of 3025 square m. How long is each side (in m)?
  9. 9.What is √9025? =
  10. 10.What is 33²? =
  11. 11.Which of these is a perfect square? (a) 796 (b) 836 (c) 784
  12. 12.What is √225? =
  13. 13.Which of these is a perfect square? (a) 1369 (b) 1371 (c) 1392
  14. 14.What is √1024? =
  15. 15.What is 32²? =
  16. 16.A square garden has an area of 361 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  18. 18.How many whole numbers lie between 37² and 38²?
  19. 19.A square garden has an area of 144 square m. How long is each side (in m)?
  20. 20.What is √1444? =
  21. 21.A square garden has an area of 1024 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 1024 (b) 1079 (c) 1028
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √2401? =
  25. 25.Which of these is a perfect square? (a) 677 (b) 710 (c) 676
  26. 26.What is √6400? =
  27. 27.What is √9801? =
  28. 28.What is √5329? =
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 16² and 17²?
  31. 31.What is 92²? =
  32. 32.What is √2704? =
  33. 33.What is 90²? =
  34. 34.A square garden has an area of 225 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 117 must be divided to get a perfect square?
  37. 37.A square garden has an area of 961 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  40. 40.What is √4761? =

Answer key

  1. 34
  2. 225
  3. 289
  4. 19
  5. 8649
  6. 30
  7. 86
  8. 55
  9. 95
  10. 1089
  11. 784
  12. 15
  13. 1369
  14. 32
  15. 1024
  16. 19
  17. 14
  18. 74
  19. 12
  20. 38
  21. 32
  22. 1024
  23. 729
  24. 49
  25. 676
  26. 80
  27. 99
  28. 73
  29. 400
  30. 32
  31. 8464
  32. 52
  33. 8100
  34. 15
  35. 11
  36. 13
  37. 31
  38. 15
  39. 15
  40. 69

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