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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 106 · 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 13 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √2401? =
  3. 3.What is 16²? =
  4. 4.What is the smallest whole number by which 63 must be divided to get a perfect square?
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √9409? =
  7. 7.What is √3481? =
  8. 8.How many whole numbers lie between 19² and 20²?
  9. 9.Which of these is a perfect square? (a) 1100 (b) 1089 (c) 1108
  10. 10.What is √5625? =
  11. 11.A square garden has an area of 1600 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 101 (b) 105 (c) 100
  13. 13.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  14. 14.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 44 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 14² and 15²?
  18. 18.How many whole numbers lie between 31² and 32²?
  19. 19.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 2304 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 36 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 529 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 26² and 27²?
  24. 24.What is 13²? =
  25. 25.Which of these is a perfect square? (a) 660 (b) 625 (c) 629
  26. 26.What is 56²? =
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √9604? =
  29. 29.How many whole numbers lie between 27² and 28²?
  30. 30.What is √5184? =
  31. 31.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  32. 32.How many whole numbers lie between 46² and 47²?
  33. 33.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 50² and 51²?
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 48² and 49²?
  38. 38.A square garden has an area of 1369 square m. How long is each side (in m)?
  39. 39.What is √961? =
  40. 40.A square garden has an area of 49 square m. How long is each side (in m)?

Answer key

  1. 169
  2. 49
  3. 256
  4. 7
  5. 289
  6. 97
  7. 59
  8. 38
  9. 1089
  10. 75
  11. 40
  12. 100
  13. 14
  14. 324
  15. 11
  16. 2
  17. 28
  18. 62
  19. 7
  20. 48
  21. 6
  22. 23
  23. 52
  24. 169
  25. 625
  26. 3136
  27. 36
  28. 98
  29. 54
  30. 72
  31. 7
  32. 92
  33. 3
  34. 11
  35. 100
  36. 49
  37. 96
  38. 37
  39. 31
  40. 7

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