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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 701 · 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 17²? =
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √6241? =
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is 83²? =
  6. 6.What is √441? =
  7. 7.How many whole numbers lie between 8² and 9²?
  8. 8.How many whole numbers lie between 30² and 31²?
  9. 9.Which of these is a perfect square? (a) 115 (b) 110 (c) 100
  10. 10.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  11. 11.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 14² and 15²?
  13. 13.Which of these is a perfect square? (a) 955 (b) 900 (c) 938
  14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 996 (b) 961 (c) 968
  16. 16.What is √3600? =
  17. 17.How many whole numbers lie between 27² and 28²?
  18. 18.A square garden has an area of 625 square m. How long is each side (in m)?
  19. 19.How many whole numbers lie between 34² and 35²?
  20. 20.What is √484? =
  21. 21.Which of these is a perfect square? (a) 576 (b) 607 (c) 596
  22. 22.A square garden has an area of 441 square m. How long is each side (in m)?
  23. 23.What is 27²? =
  24. 24.A square garden has an area of 1849 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 60 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.What is the smallest whole number by which 891 must be divided to get a perfect square?
  28. 28.Which of these is a perfect square? (a) 324 (b) 349 (c) 334
  29. 29.Which of these is a perfect square? (a) 640 (b) 650 (c) 625
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  31. 31.How many whole numbers lie between 13² and 14²?
  32. 32.A square garden has an area of 3136 square m. How long is each side (in m)?
  33. 33.What is √961? =
  34. 34.Which of these is a perfect square? (a) 1600 (b) 1605 (c) 1653
  35. 35.What is 71²? =
  36. 36.How many whole numbers lie between 35² and 36²?
  37. 37.What is the smallest whole number by which 8 must be divided to get a perfect square?
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.What is 77²? =
  40. 40.What is the smallest whole number by which 128 must be divided to get a perfect square?

Answer key

  1. 289
  2. 289
  3. 79
  4. 144
  5. 6889
  6. 21
  7. 16
  8. 60
  9. 100
  10. 11
  11. 15
  12. 28
  13. 900
  14. 25
  15. 961
  16. 60
  17. 54
  18. 25
  19. 68
  20. 22
  21. 576
  22. 21
  23. 729
  24. 43
  25. 15
  26. 86
  27. 11
  28. 324
  29. 625
  30. 324
  31. 26
  32. 56
  33. 31
  34. 1600
  35. 5041
  36. 70
  37. 2
  38. 54
  39. 5929
  40. 2

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