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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 650 · 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) 1493 (b) 1444 (c) 1452
  2. 2.Which of these is a perfect square? (a) 576 (b) 609 (c) 611
  3. 3.What is √5329? =
  4. 4.A square garden has an area of 2304 square m. How long is each side (in m)?
  5. 5.How many whole numbers lie between 48² and 49²?
  6. 6.A square garden has an area of 1156 square m. How long is each side (in m)?
  7. 7.What is 40²? =
  8. 8.How many whole numbers lie between 42² and 43²?
  9. 9.What is 15²? =
  10. 10.What is √289? =
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 82²? =
  13. 13.How many whole numbers lie between 47² and 48²?
  14. 14.Which of these is a perfect square? (a) 537 (b) 529 (c) 572
  15. 15.What is √9801? =
  16. 16.What is 69²? =
  17. 17.How many whole numbers lie between 50² and 51²?
  18. 18.What is 34²? =
  19. 19.What is 13²? =
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 1234 (b) 1286 (c) 1225
  22. 22.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  23. 23.What is 31²? =
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 2025 square m. How long is each side (in m)?
  26. 26.What is 27²? =
  27. 27.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  28. 28.What is √1369? =
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √2601? =
  31. 31.What is √8281? =
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  34. 34.What is √1521? =
  35. 35.What is √5184? =
  36. 36.What is √2916? =
  37. 37.A square garden has an area of 1089 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 16² and 17²?
  40. 40.How many whole numbers lie between 35² and 36²?

Answer key

  1. 1444
  2. 576
  3. 73
  4. 48
  5. 96
  6. 34
  7. 1600
  8. 84
  9. 225
  10. 17
  11. 625
  12. 6724
  13. 94
  14. 529
  15. 99
  16. 4761
  17. 100
  18. 1156
  19. 169
  20. 361
  21. 1225
  22. 15
  23. 961
  24. 676
  25. 45
  26. 729
  27. 2
  28. 37
  29. 289
  30. 51
  31. 91
  32. 6
  33. 2
  34. 39
  35. 72
  36. 54
  37. 33
  38. 54
  39. 32
  40. 70

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