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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 110 · 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.What is 32²? =
  2. 2.Which of these is a perfect square? (a) 1573 (b) 1521 (c) 1546
  3. 3.A square garden has an area of 2601 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 32 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 529 (b) 550 (c) 568
  6. 6.What is 93²? =
  7. 7.Which of these is a perfect square? (a) 100 (b) 103 (c) 116
  8. 8.What is √529? =
  9. 9.How many whole numbers lie between 13² and 14²?
  10. 10.How many whole numbers lie between 32² and 33²?
  11. 11.How many whole numbers lie between 10² and 11²?
  12. 12.How many whole numbers lie between 6² and 7²?
  13. 13.What is √6241? =
  14. 14.What is √2025? =
  15. 15.A square garden has an area of 3481 square m. How long is each side (in m)?
  16. 16.What is √9801? =
  17. 17.What is √6400? =
  18. 18.Which of these is a perfect square? (a) 484 (b) 485 (c) 516
  19. 19.What is √3136? =
  20. 20.Which of these is a perfect square? (a) 1287 (b) 1276 (c) 1225
  21. 21.What is 67²? =
  22. 22.Which of these is a perfect square? (a) 380 (b) 386 (c) 361
  23. 23.What is √8464? =
  24. 24.What is 42²? =
  25. 25.What is 98²? =
  26. 26.What is 33²? =
  27. 27.Which of these is a perfect square? (a) 360 (b) 327 (c) 324
  28. 28.What is the smallest whole number by which 250 must be divided to get a perfect square?
  29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √225? =
  32. 32.Which of these is a perfect square? (a) 625 (b) 653 (c) 647
  33. 33.What is 43²? =
  34. 34.What is 86²? =
  35. 35.What is 54²? =
  36. 36.What is √1024? =
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.How many whole numbers lie between 12² and 13²?
  40. 40.What is 87²? =

Answer key

  1. 1024
  2. 1521
  3. 51
  4. 2
  5. 529
  6. 8649
  7. 100
  8. 23
  9. 26
  10. 64
  11. 20
  12. 12
  13. 79
  14. 45
  15. 59
  16. 99
  17. 80
  18. 484
  19. 56
  20. 1225
  21. 4489
  22. 361
  23. 92
  24. 1764
  25. 9604
  26. 1089
  27. 324
  28. 10
  29. 169
  30. 900
  31. 15
  32. 625
  33. 1849
  34. 7396
  35. 2916
  36. 32
  37. 121
  38. 60
  39. 24
  40. 7569

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