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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 429 · 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 10 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 217 (b) 196 (c) 203
  3. 3.What is √7921? =
  4. 4.How many whole numbers lie between 27² and 28²?
  5. 5.What is √7569? =
  6. 6.How many whole numbers lie between 37² and 38²?
  7. 7.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  8. 8.What is the smallest whole number by which 810 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 19² and 20²?
  10. 10.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 888 (b) 841 (c) 844
  12. 12.What is √1225? =
  13. 13.What is 46²? =
  14. 14.A square garden has an area of 625 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 44 must be divided to get a perfect square?
  16. 16.What is √625? =
  17. 17.What is 42²? =
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 74²? =
  20. 20.A square garden has an area of 1764 square m. How long is each side (in m)?
  21. 21.What is √5929? =
  22. 22.What is 14²? =
  23. 23.A square garden has an area of 2704 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 17² and 18²?
  25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 29² and 30²?
  27. 27.A square garden has an area of 3136 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 49 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 18 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 50 must be divided to get a perfect square?
  31. 31.A square garden has an area of 2209 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 42² and 43²?
  33. 33.What is 91²? =
  34. 34.How many whole numbers lie between 7² and 8²?
  35. 35.How many whole numbers lie between 34² and 35²?
  36. 36.Which of these is a perfect square? (a) 945 (b) 918 (c) 900
  37. 37.Which of these is a perfect square? (a) 177 (b) 169 (c) 189
  38. 38.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 815 (b) 784 (c) 786
  40. 40.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 100
  2. 196
  3. 89
  4. 54
  5. 87
  6. 74
  7. 14
  8. 10
  9. 38
  10. 3
  11. 841
  12. 35
  13. 2116
  14. 25
  15. 11
  16. 25
  17. 1764
  18. 225
  19. 5476
  20. 42
  21. 77
  22. 196
  23. 52
  24. 34
  25. 576
  26. 58
  27. 56
  28. 7
  29. 2
  30. 2
  31. 47
  32. 84
  33. 8281
  34. 14
  35. 68
  36. 900
  37. 169
  38. 5
  39. 784
  40. 256

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