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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 403 · 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 16² and 17²?
  2. 2.What is 83²? =
  3. 3.How many whole numbers lie between 44² and 45²?
  4. 4.How many whole numbers lie between 18² and 19²?
  5. 5.Which of these is a perfect square? (a) 256 (b) 259 (c) 282
  6. 6.What is √1681? =
  7. 7.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 225 (b) 248 (c) 245
  10. 10.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 1101 (b) 1102 (c) 1089
  12. 12.Which of these is a perfect square? (a) 900 (b) 953 (c) 904
  13. 13.A square garden has an area of 2601 square m. How long is each side (in m)?
  14. 14.What is 16²? =
  15. 15.A square garden has an area of 2916 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √9801? =
  18. 18.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  19. 19.What is √1369? =
  20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √2704? =
  22. 22.How many whole numbers lie between 38² and 39²?
  23. 23.What is 93²? =
  24. 24.How many whole numbers lie between 14² and 15²?
  25. 25.Which of these is a perfect square? (a) 675 (b) 643 (c) 625
  26. 26.What is 50²? =
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 898 (b) 857 (c) 841
  29. 29.How many whole numbers lie between 17² and 18²?
  30. 30.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  31. 31.A square garden has an area of 576 square m. How long is each side (in m)?
  32. 32.What is √484? =
  33. 33.What is the smallest whole number by which 48 must be divided to get a perfect square?
  34. 34.How many whole numbers lie between 20² and 21²?
  35. 35.A square garden has an area of 441 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 12² and 13²?
  37. 37.What is the smallest whole number by which 56 must be divided to get a perfect square?
  38. 38.Which of these is a perfect square? (a) 170 (b) 169 (c) 178
  39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 21²? =

Answer key

  1. 32
  2. 6889
  3. 88
  4. 36
  5. 256
  6. 41
  7. 576
  8. 784
  9. 225
  10. 2
  11. 1089
  12. 900
  13. 51
  14. 256
  15. 54
  16. 144
  17. 99
  18. 7
  19. 37
  20. 484
  21. 52
  22. 76
  23. 8649
  24. 28
  25. 625
  26. 2500
  27. 225
  28. 841
  29. 34
  30. 5
  31. 24
  32. 22
  33. 3
  34. 40
  35. 21
  36. 24
  37. 14
  38. 169
  39. 100
  40. 441

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