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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 570 · 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.How many whole numbers lie between 7² and 8²?
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 1024 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 2304 square m. How long is each side (in m)?
  5. 5.What is 57²? =
  6. 6.What is √3600? =
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 17² and 18²?
  9. 9.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 1445 (b) 1444 (c) 1501
  11. 11.A square garden has an area of 289 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 469 (b) 441 (c) 442
  13. 13.How many whole numbers lie between 39² and 40²?
  14. 14.A square garden has an area of 49 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 25 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 2500 square m. How long is each side (in m)?
  17. 17.What is 77²? =
  18. 18.Which of these is a perfect square? (a) 1211 (b) 1219 (c) 1156
  19. 19.Which of these is a perfect square? (a) 400 (b) 432 (c) 418
  20. 20.How many whole numbers lie between 34² and 35²?
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 27 must be divided to get a perfect square?
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 38²? =
  25. 25.What is √7056? =
  26. 26.A square garden has an area of 625 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  28. 28.How many whole numbers lie between 16² and 17²?
  29. 29.What is 16²? =
  30. 30.A square garden has an area of 484 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 1623 (b) 1629 (c) 1600
  32. 32.A square garden has an area of 3025 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 900 square m. How long is each side (in m)?
  34. 34.What is √169? =
  35. 35.What is 26²? =
  36. 36.A square garden has an area of 225 square m. How long is each side (in m)?
  37. 37.What is √3481? =
  38. 38.A square garden has an area of 1681 square m. How long is each side (in m)?
  39. 39.What is √196? =
  40. 40.How many whole numbers lie between 38² and 39²?

Answer key

  1. 14
  2. 144
  3. 32
  4. 48
  5. 3249
  6. 60
  7. 81
  8. 34
  9. 729
  10. 1444
  11. 17
  12. 441
  13. 78
  14. 7
  15. 5
  16. 50
  17. 5929
  18. 1156
  19. 400
  20. 68
  21. 100
  22. 3
  23. 841
  24. 1444
  25. 84
  26. 25
  27. 14
  28. 32
  29. 256
  30. 22
  31. 1600
  32. 55
  33. 30
  34. 13
  35. 676
  36. 15
  37. 59
  38. 41
  39. 14
  40. 76

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