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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 497 · 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 405 must be divided to get a perfect square?
  2. 2.A square garden has an area of 2704 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 484 (b) 516 (c) 497
  4. 4.What is the smallest whole number by which 18 must be divided to get a perfect square?
  5. 5.How many whole numbers lie between 13² and 14²?
  6. 6.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 1466 (b) 1474 (c) 1444
  8. 8.What is 60²? =
  9. 9.Which of these is a perfect square? (a) 1225 (b) 1231 (c) 1236
  10. 10.How many whole numbers lie between 36² and 37²?
  11. 11.What is 17²? =
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 47² and 48²?
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 377 (b) 379 (c) 361
  16. 16.How many whole numbers lie between 27² and 28²?
  17. 17.What is √5625? =
  18. 18.How many whole numbers lie between 22² and 23²?
  19. 19.How many whole numbers lie between 20² and 21²?
  20. 20.What is the smallest whole number by which 24 must be divided to get a perfect square?
  21. 21.What is √3136? =
  22. 22.What is 58²? =
  23. 23.How many whole numbers lie between 40² and 41²?
  24. 24.What is √3600? =
  25. 25.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 44² and 45²?
  28. 28.What is the smallest whole number by which 20 must be divided to get a perfect square?
  29. 29.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  30. 30.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 1296 (b) 1315 (c) 1314
  32. 32.What is the smallest whole number by which 243 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 30² and 31²?
  34. 34.What is √1681? =
  35. 35.Which of these is a perfect square? (a) 103 (b) 100 (c) 109
  36. 36.How many whole numbers lie between 7² and 8²?
  37. 37.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  38. 38.A square garden has an area of 2025 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 150 must be divided to get a perfect square?

Answer key

  1. 5
  2. 52
  3. 484
  4. 2
  5. 26
  6. 15
  7. 1444
  8. 3600
  9. 1225
  10. 72
  11. 289
  12. 25
  13. 94
  14. 784
  15. 361
  16. 54
  17. 75
  18. 44
  19. 40
  20. 6
  21. 56
  22. 3364
  23. 80
  24. 60
  25. 529
  26. 324
  27. 88
  28. 5
  29. 7
  30. 11
  31. 1296
  32. 3
  33. 60
  34. 41
  35. 100
  36. 14
  37. 14
  38. 45
  39. 10
  40. 6

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