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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 460 · 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 16² and 17²?
  2. 2.A square garden has an area of 36 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 64 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  5. 5.What is 73²? =
  6. 6.A square garden has an area of 2704 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 99 must be divided to get a perfect square?
  8. 8.What is 53²? =
  9. 9.How many whole numbers lie between 43² and 44²?
  10. 10.How many whole numbers lie between 20² and 21²?
  11. 11.How many whole numbers lie between 36² and 37²?
  12. 12.Which of these is a perfect square? (a) 604 (b) 617 (c) 576
  13. 13.A square garden has an area of 100 square m. How long is each side (in m)?
  14. 14.What is 21²? =
  15. 15.A square garden has an area of 961 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 640 must be divided to get a perfect square?
  17. 17.What is √2401? =
  18. 18.Which of these is a perfect square? (a) 484 (b) 526 (c) 515
  19. 19.What is √9604? =
  20. 20.What is √1156? =
  21. 21.What is 35²? =
  22. 22.What is the smallest whole number by which 832 must be divided to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 353 (b) 347 (c) 324
  24. 24.What is the sum of the first 14 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.Which of these is a perfect square? (a) 169 (b) 172 (c) 193
  27. 27.What is √196? =
  28. 28.What is √8281? =
  29. 29.A square garden has an area of 2809 square m. How long is each side (in m)?
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 13²? =
  32. 32.What is 22²? =
  33. 33.What is √5776? =
  34. 34.Which of these is a perfect square? (a) 417 (b) 400 (c) 436
  35. 35.A square garden has an area of 3481 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 1156 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 117 must be divided to get a perfect square?
  38. 38.What is √4225? =
  39. 39.Which of these is a perfect square? (a) 963 (b) 993 (c) 961
  40. 40.How many whole numbers lie between 41² and 42²?

Answer key

  1. 32
  2. 6
  3. 8
  4. 2
  5. 5329
  6. 52
  7. 11
  8. 2809
  9. 86
  10. 40
  11. 72
  12. 576
  13. 10
  14. 441
  15. 31
  16. 10
  17. 49
  18. 484
  19. 98
  20. 34
  21. 1225
  22. 13
  23. 324
  24. 196
  25. 45
  26. 169
  27. 14
  28. 91
  29. 53
  30. 144
  31. 169
  32. 484
  33. 76
  34. 400
  35. 59
  36. 34
  37. 13
  38. 65
  39. 961
  40. 82

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