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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 302 · 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 sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 11²? =
  4. 4.How many whole numbers lie between 20² and 21²?
  5. 5.What is √1600? =
  6. 6.What is √3249? =
  7. 7.What is the smallest whole number by which 63 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  9. 9.What is √1296? =
  10. 10.Which of these is a perfect square? (a) 220 (b) 208 (c) 196
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 50² and 51²?
  13. 13.What is 94²? =
  14. 14.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 1681 square m. How long is each side (in m)?
  16. 16.What is √676? =
  17. 17.What is 20²? =
  18. 18.Which of these is a perfect square? (a) 426 (b) 403 (c) 400
  19. 19.How many whole numbers lie between 9² and 10²?
  20. 20.How many whole numbers lie between 12² and 13²?
  21. 21.A square garden has an area of 2601 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 441 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 1116 (b) 1089 (c) 1144
  24. 24.What is √256? =
  25. 25.What is 81²? =
  26. 26.How many whole numbers lie between 25² and 26²?
  27. 27.What is 12²? =
  28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 1600 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  31. 31.A square garden has an area of 169 square m. How long is each side (in m)?
  32. 32.What is 57²? =
  33. 33.What is 29²? =
  34. 34.What is the smallest whole number by which 810 must be divided to get a perfect square?
  35. 35.What is √8100? =
  36. 36.What is √1444? =
  37. 37.What is 60²? =
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 225 square m. How long is each side (in m)?

Answer key

  1. 900
  2. 25
  3. 121
  4. 40
  5. 40
  6. 57
  7. 7
  8. 6
  9. 36
  10. 196
  11. 49
  12. 100
  13. 8836
  14. 2
  15. 41
  16. 26
  17. 400
  18. 400
  19. 18
  20. 24
  21. 51
  22. 21
  23. 1089
  24. 16
  25. 6561
  26. 50
  27. 144
  28. 81
  29. 40
  30. 361
  31. 13
  32. 3249
  33. 841
  34. 10
  35. 90
  36. 38
  37. 3600
  38. 64
  39. 42
  40. 15

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