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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 193 · 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.A square garden has an area of 49 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 106 (b) 105 (c) 100
  3. 3.A square garden has an area of 676 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  5. 5.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 1296 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 126 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  9. 9.What is 33²? =
  10. 10.A square garden has an area of 196 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 40 must be divided to get a perfect square?
  13. 13.How many whole numbers lie between 37² and 38²?
  14. 14.A square garden has an area of 3364 square m. How long is each side (in m)?
  15. 15.What is 38²? =
  16. 16.Which of these is a perfect square? (a) 900 (b) 931 (c) 922
  17. 17.Which of these is a perfect square? (a) 169 (b) 194 (c) 172
  18. 18.What is √961? =
  19. 19.What is 74²? =
  20. 20.Which of these is a perfect square? (a) 1358 (b) 1327 (c) 1296
  21. 21.Which of these is a perfect square? (a) 268 (b) 270 (c) 256
  22. 22.How many whole numbers lie between 7² and 8²?
  23. 23.What is the smallest whole number by which 245 must be divided to get a perfect square?
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 5² and 6²?
  26. 26.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  27. 27.What is √3721? =
  28. 28.What is 59²? =
  29. 29.What is the smallest whole number by which 147 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 15²? =
  33. 33.What is √8281? =
  34. 34.A square garden has an area of 2601 square m. How long is each side (in m)?
  35. 35.What is √225? =
  36. 36.A square garden has an area of 3600 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 21² and 22²?
  38. 38.What is √2209? =
  39. 39.How many whole numbers lie between 34² and 35²?
  40. 40.How many whole numbers lie between 38² and 39²?

Answer key

  1. 7
  2. 100
  3. 26
  4. 5
  5. 10
  6. 36
  7. 14
  8. 11
  9. 1089
  10. 14
  11. 81
  12. 10
  13. 74
  14. 58
  15. 1444
  16. 900
  17. 169
  18. 31
  19. 5476
  20. 1296
  21. 256
  22. 14
  23. 5
  24. 144
  25. 10
  26. 15
  27. 61
  28. 3481
  29. 3
  30. 13
  31. 625
  32. 225
  33. 91
  34. 51
  35. 15
  36. 60
  37. 42
  38. 47
  39. 68
  40. 76

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