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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 362 · 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) 1631 (b) 1600 (c) 1612
  2. 2.Which of these is a perfect square? (a) 121 (b) 143 (c) 126
  3. 3.What is 11²? =
  4. 4.What is 62²? =
  5. 5.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 328 (b) 324 (c) 333
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 234 (b) 248 (c) 225
  9. 9.How many whole numbers lie between 32² and 33²?
  10. 10.How many whole numbers lie between 31² and 32²?
  11. 11.How many whole numbers lie between 6² and 7²?
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 676 square m. How long is each side (in m)?
  14. 14.What is 60²? =
  15. 15.A square garden has an area of 36 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1206 (b) 1183 (c) 1156
  18. 18.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √961? =
  20. 20.How many whole numbers lie between 7² and 8²?
  21. 21.Which of these is a perfect square? (a) 438 (b) 400 (c) 411
  22. 22.What is the smallest whole number by which 360 must be divided to get a perfect square?
  23. 23.A square garden has an area of 100 square m. How long is each side (in m)?
  24. 24.What is √7396? =
  25. 25.How many whole numbers lie between 35² and 36²?
  26. 26.A square garden has an area of 256 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 56 must be divided to get a perfect square?
  28. 28.Which of these is a perfect square? (a) 179 (b) 170 (c) 169
  29. 29.What is √3969? =
  30. 30.How many whole numbers lie between 19² and 20²?
  31. 31.What is √6889? =
  32. 32.How many whole numbers lie between 8² and 9²?
  33. 33.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 400 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 625 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 1369 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 2025 square m. How long is each side (in m)?
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √841? =
  40. 40.What is 23²? =

Answer key

  1. 1600
  2. 121
  3. 121
  4. 3844
  5. 729
  6. 324
  7. 900
  8. 225
  9. 64
  10. 62
  11. 12
  12. 196
  13. 26
  14. 3600
  15. 6
  16. 5
  17. 1156
  18. 784
  19. 31
  20. 14
  21. 400
  22. 10
  23. 10
  24. 86
  25. 70
  26. 16
  27. 14
  28. 169
  29. 63
  30. 38
  31. 83
  32. 16
  33. 289
  34. 20
  35. 25
  36. 37
  37. 45
  38. 576
  39. 29
  40. 529

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