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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 15 · 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.Which of these is a perfect square? (a) 335 (b) 331 (c) 324
  2. 2.What is √1089? =
  3. 3.What is the smallest whole number by which 96 must be divided to get a perfect square?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 36² and 37²?
  6. 6.Which of these is a perfect square? (a) 468 (b) 450 (c) 441
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.A square garden has an area of 2401 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 1168 (b) 1176 (c) 1156
  12. 12.What is 81²? =
  13. 13.A square garden has an area of 900 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 859 (b) 841 (c) 878
  15. 15.What is √2304? =
  16. 16.How many whole numbers lie between 45² and 46²?
  17. 17.What is the smallest whole number by which 637 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 60 must be divided to get a perfect square?
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 80 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 1115 (b) 1089 (c) 1143
  22. 22.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
  24. 24.What is 85²? =
  25. 25.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √1156? =
  28. 28.Which of these is a perfect square? (a) 711 (b) 676 (c) 716
  29. 29.What is 18²? =
  30. 30.What is √1600? =
  31. 31.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 367 (b) 361 (c) 394
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 72 must be divided to get a perfect square?
  36. 36.What is 29²? =
  37. 37.How many whole numbers lie between 30² and 31²?
  38. 38.What is the smallest whole number by which 468 must be divided to get a perfect square?
  39. 39.A square garden has an area of 2209 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 324
  2. 33
  3. 6
  4. 121
  5. 72
  6. 441
  7. 64
  8. 49
  9. 3
  10. 400
  11. 1156
  12. 6561
  13. 30
  14. 841
  15. 48
  16. 90
  17. 13
  18. 15
  19. 225
  20. 5
  21. 1089
  22. 64
  23. 7
  24. 7225
  25. 6
  26. 169
  27. 34
  28. 676
  29. 324
  30. 40
  31. 14
  32. 11
  33. 361
  34. 144
  35. 2
  36. 841
  37. 60
  38. 13
  39. 47
  40. 324

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