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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 63 · 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) 108 (b) 102 (c) 100
  2. 2.What is √1600? =
  3. 3.A square garden has an area of 2401 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 48² and 49²?
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 576 (b) 607 (c) 582
  7. 7.Which of these is a perfect square? (a) 1087 (b) 1060 (c) 1024
  8. 8.What is 79²? =
  9. 9.How many whole numbers lie between 38² and 39²?
  10. 10.A square garden has an area of 2209 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 320 must be divided to get a perfect square?
  12. 12.What is √8100? =
  13. 13.What is the smallest whole number by which 98 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 716 (b) 676 (c) 710
  15. 15.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  16. 16.What is the smallest whole number by which 175 must be divided to get a perfect square?
  17. 17.What is the smallest whole number by which 704 must be divided to get a perfect square?
  18. 18.What is √676? =
  19. 19.A square garden has an area of 49 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is 91²? =
  22. 22.A square garden has an area of 1296 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 24² and 25²?
  24. 24.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  25. 25.A square garden has an area of 36 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1127 (b) 1089 (c) 1123
  27. 27.How many whole numbers lie between 50² and 51²?
  28. 28.What is 98²? =
  29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √3364? =
  32. 32.A square garden has an area of 2500 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 7² and 8²?
  34. 34.How many whole numbers lie between 46² and 47²?
  35. 35.What is 67²? =
  36. 36.A square garden has an area of 196 square m. How long is each side (in m)?
  37. 37.What is 81²? =
  38. 38.What is √7225? =
  39. 39.What is √4489? =
  40. 40.Which of these is a perfect square? (a) 1476 (b) 1444 (c) 1517

Answer key

  1. 100
  2. 40
  3. 49
  4. 96
  5. 676
  6. 576
  7. 1024
  8. 6241
  9. 76
  10. 47
  11. 5
  12. 90
  13. 2
  14. 676
  15. 13
  16. 7
  17. 11
  18. 26
  19. 7
  20. 576
  21. 8281
  22. 36
  23. 48
  24. 6
  25. 6
  26. 1089
  27. 100
  28. 9604
  29. 784
  30. 225
  31. 58
  32. 50
  33. 14
  34. 92
  35. 4489
  36. 14
  37. 6561
  38. 85
  39. 67
  40. 1444

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