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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 443 · 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.A square garden has an area of 2704 square m. How long is each side (in m)?
  2. 2.What is 76²? =
  3. 3.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  4. 4.A square garden has an area of 225 square m. How long is each side (in m)?
  5. 5.What is 23²? =
  6. 6.Which of these is a perfect square? (a) 198 (b) 220 (c) 196
  7. 7.What is 37²? =
  8. 8.What is 94²? =
  9. 9.How many whole numbers lie between 16² and 17²?
  10. 10.A square garden has an area of 1369 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 1675 (b) 1680 (c) 1600
  12. 12.A square garden has an area of 196 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 28² and 29²?
  14. 14.Which of these is a perfect square? (a) 529 (b) 567 (c) 558
  15. 15.Which of these is a perfect square? (a) 1230 (b) 1225 (c) 1250
  16. 16.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  17. 17.What is √6561? =
  18. 18.What is 95²? =
  19. 19.A square garden has an area of 81 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 11² and 12²?
  21. 21.Which of these is a perfect square? (a) 1485 (b) 1492 (c) 1444
  22. 22.Which of these is a perfect square? (a) 317 (b) 319 (c) 289
  23. 23.A square garden has an area of 400 square m. How long is each side (in m)?
  24. 24.What is √1156? =
  25. 25.What is 73²? =
  26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √9801? =
  28. 28.What is the smallest whole number by which 160 must be divided to get a perfect square?
  29. 29.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  30. 30.What is √8464? =
  31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
  32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 22² and 23²?
  34. 34.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 9² and 10²?
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 405 must be divided to get a perfect square?
  38. 38.What is 26²? =
  39. 39.Which of these is a perfect square? (a) 185 (b) 170 (c) 169
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 52
  2. 5776
  3. 7
  4. 15
  5. 529
  6. 196
  7. 1369
  8. 8836
  9. 32
  10. 37
  11. 1600
  12. 14
  13. 56
  14. 529
  15. 1225
  16. 6
  17. 81
  18. 9025
  19. 9
  20. 22
  21. 1444
  22. 289
  23. 20
  24. 34
  25. 5329
  26. 361
  27. 99
  28. 10
  29. 13
  30. 92
  31. 46
  32. 81
  33. 44
  34. 15
  35. 18
  36. 144
  37. 5
  38. 676
  39. 169
  40. 100

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