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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 217 · 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 21² and 22²?
  2. 2.What is the smallest whole number by which 12 must be divided to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 464 (b) 453 (c) 441
  4. 4.How many whole numbers lie between 9² and 10²?
  5. 5.What is √9409? =
  6. 6.How many whole numbers lie between 17² and 18²?
  7. 7.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  9. 9.Which of these is a perfect square? (a) 398 (b) 399 (c) 361
  10. 10.What is the smallest whole number by which 216 must be divided to get a perfect square?
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  13. 13.What is 35²? =
  14. 14.How many whole numbers lie between 34² and 35²?
  15. 15.What is 37²? =
  16. 16.A square garden has an area of 2116 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 41² and 42²?
  18. 18.What is √3364? =
  19. 19.Which of these is a perfect square? (a) 191 (b) 182 (c) 169
  20. 20.What is 57²? =
  21. 21.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 43² and 44²?
  23. 23.A square garden has an area of 2209 square m. How long is each side (in m)?
  24. 24.What is 84²? =
  25. 25.What is 75²? =
  26. 26.How many whole numbers lie between 38² and 39²?
  27. 27.What is √9025? =
  28. 28.Which of these is a perfect square? (a) 687 (b) 676 (c) 704
  29. 29.A square garden has an area of 961 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 1272 (b) 1225 (c) 1273
  31. 31.Which of these is a perfect square? (a) 842 (b) 883 (c) 841
  32. 32.How many whole numbers lie between 23² and 24²?
  33. 33.What is √4900? =
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  35. 35.Which of these is a perfect square? (a) 206 (b) 209 (c) 196
  36. 36.What is √6241? =
  37. 37.What is √7396? =
  38. 38.A square garden has an area of 81 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 1052 (b) 1081 (c) 1024
  40. 40.A square garden has an area of 1369 square m. How long is each side (in m)?

Answer key

  1. 42
  2. 3
  3. 441
  4. 18
  5. 97
  6. 34
  7. 576
  8. 2
  9. 361
  10. 6
  11. 361
  12. 15
  13. 1225
  14. 68
  15. 1369
  16. 46
  17. 82
  18. 58
  19. 169
  20. 3249
  21. 900
  22. 86
  23. 47
  24. 7056
  25. 5625
  26. 76
  27. 95
  28. 676
  29. 31
  30. 1225
  31. 841
  32. 46
  33. 70
  34. 841
  35. 196
  36. 79
  37. 86
  38. 9
  39. 1024
  40. 37

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