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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 141 · 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) 1600 (b) 1633 (c) 1626
  2. 2.Which of these is a perfect square? (a) 1197 (b) 1156 (c) 1183
  3. 3.What is √1225? =
  4. 4.What is √6561? =
  5. 5.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 106 (b) 100 (c) 114
  7. 7.What is √484? =
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 1296 square m. How long is each side (in m)?
  10. 10.What is √9409? =
  11. 11.Which of these is a perfect square? (a) 196 (b) 210 (c) 201
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  14. 14.What is 32²? =
  15. 15.What is √9801? =
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √3136? =
  18. 18.How many whole numbers lie between 41² and 42²?
  19. 19.What is 19²? =
  20. 20.How many whole numbers lie between 28² and 29²?
  21. 21.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 529 square m. How long is each side (in m)?
  23. 23.What is √289? =
  24. 24.A square garden has an area of 1600 square m. How long is each side (in m)?
  25. 25.What is √7744? =
  26. 26.Which of these is a perfect square? (a) 256 (b) 286 (c) 278
  27. 27.What is 81²? =
  28. 28.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  29. 29.A square garden has an area of 2116 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 18² and 19²?
  31. 31.How many whole numbers lie between 23² and 24²?
  32. 32.Which of these is a perfect square? (a) 1275 (b) 1227 (c) 1225
  33. 33.A square garden has an area of 324 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 1082 (b) 1024 (c) 1037
  35. 35.What is √961? =
  36. 36.A square garden has an area of 225 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 2916 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 1395 (b) 1369 (c) 1428
  39. 39.A square garden has an area of 484 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 49² and 50²?

Answer key

  1. 1600
  2. 1156
  3. 35
  4. 81
  5. 5
  6. 100
  7. 22
  8. 196
  9. 36
  10. 97
  11. 196
  12. 25
  13. 13
  14. 1024
  15. 99
  16. 64
  17. 56
  18. 82
  19. 361
  20. 56
  21. 529
  22. 23
  23. 17
  24. 40
  25. 88
  26. 256
  27. 6561
  28. 6
  29. 46
  30. 36
  31. 46
  32. 1225
  33. 18
  34. 1024
  35. 31
  36. 15
  37. 54
  38. 1369
  39. 22
  40. 98

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