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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 505 · 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 11 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 1849 square m. How long is each side (in m)?
  4. 4.What is 33²? =
  5. 5.Which of these is a perfect square? (a) 333 (b) 346 (c) 324
  6. 6.How many whole numbers lie between 42² and 43²?
  7. 7.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  8. 8.What is √625? =
  9. 9.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 14² and 15²?
  11. 11.A square garden has an area of 100 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  13. 13.Which of these is a perfect square? (a) 1093 (b) 1089 (c) 1120
  14. 14.How many whole numbers lie between 30² and 31²?
  15. 15.Which of these is a perfect square? (a) 218 (b) 223 (c) 196
  16. 16.How many whole numbers lie between 37² and 38²?
  17. 17.A square garden has an area of 3481 square m. How long is each side (in m)?
  18. 18.What is √4900? =
  19. 19.What is √1369? =
  20. 20.What is 88²? =
  21. 21.Which of these is a perfect square? (a) 1478 (b) 1449 (c) 1444
  22. 22.How many whole numbers lie between 6² and 7²?
  23. 23.How many whole numbers lie between 36² and 37²?
  24. 24.What is √2601? =
  25. 25.A square garden has an area of 900 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  28. 28.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  29. 29.How many whole numbers lie between 23² and 24²?
  30. 30.Which of these is a perfect square? (a) 165 (b) 144 (c) 149
  31. 31.A square garden has an area of 225 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 27 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  35. 35.What is √5184? =
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 22² and 23²?
  38. 38.What is 31²? =
  39. 39.What is √1521? =
  40. 40.What is √841? =

Answer key

  1. 121
  2. 100
  3. 43
  4. 1089
  5. 324
  6. 84
  7. 7
  8. 25
  9. 3
  10. 28
  11. 10
  12. 256
  13. 1089
  14. 60
  15. 196
  16. 74
  17. 59
  18. 70
  19. 37
  20. 7744
  21. 1444
  22. 12
  23. 72
  24. 51
  25. 30
  26. 225
  27. 7
  28. 3
  29. 46
  30. 144
  31. 15
  32. 3
  33. 15
  34. 11
  35. 72
  36. 625
  37. 44
  38. 961
  39. 39
  40. 29

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