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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 38 · 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) 374 (b) 361 (c) 362
  2. 2.Which of these is a perfect square? (a) 541 (b) 555 (c) 529
  3. 3.What is √7225? =
  4. 4.A square garden has an area of 1681 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 2809 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 779 (b) 761 (c) 729
  7. 7.Which of these is a perfect square? (a) 108 (b) 106 (c) 100
  8. 8.How many whole numbers lie between 17² and 18²?
  9. 9.What is the smallest whole number by which 735 must be divided to get a perfect square?
  10. 10.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 2401 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 22² and 23²?
  14. 14.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  15. 15.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  16. 16.What is √1156? =
  17. 17.How many whole numbers lie between 7² and 8²?
  18. 18.What is √7921? =
  19. 19.How many whole numbers lie between 46² and 47²?
  20. 20.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 67²? =
  23. 23.Which of these is a perfect square? (a) 123 (b) 121 (c) 136
  24. 24.What is √676? =
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 13² and 14²?
  27. 27.Which of these is a perfect square? (a) 186 (b) 169 (c) 171
  28. 28.A square garden has an area of 36 square m. How long is each side (in m)?
  29. 29.What is √4489? =
  30. 30.What is the smallest whole number by which 468 must be divided to get a perfect square?
  31. 31.What is √1089? =
  32. 32.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  33. 33.What is 18²? =
  34. 34.What is √4624? =
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is √5476? =
  37. 37.What is 69²? =
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 1444 square m. How long is each side (in m)?
  40. 40.What is 60²? =

Answer key

  1. 361
  2. 529
  3. 85
  4. 41
  5. 53
  6. 729
  7. 100
  8. 34
  9. 15
  10. 7
  11. 49
  12. 729
  13. 44
  14. 15
  15. 10
  16. 34
  17. 14
  18. 89
  19. 92
  20. 2
  21. 324
  22. 4489
  23. 121
  24. 26
  25. 256
  26. 26
  27. 169
  28. 6
  29. 67
  30. 13
  31. 33
  32. 5
  33. 324
  34. 68
  35. 841
  36. 74
  37. 4761
  38. 49
  39. 38
  40. 3600

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