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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 112 · 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 35² and 36²?
  2. 2.Which of these is a perfect square? (a) 188 (b) 180 (c) 169
  3. 3.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  4. 4.How many whole numbers lie between 16² and 17²?
  5. 5.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  6. 6.What is √1089? =
  7. 7.What is √1296? =
  8. 8.What is √961? =
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 1062 (b) 1086 (c) 1024
  11. 11.A square garden has an area of 81 square m. How long is each side (in m)?
  12. 12.What is 75²? =
  13. 13.How many whole numbers lie between 43² and 44²?
  14. 14.What is √6400? =
  15. 15.What is √576? =
  16. 16.How many whole numbers lie between 45² and 46²?
  17. 17.What is √4900? =
  18. 18.Which of these is a perfect square? (a) 144 (b) 167 (c) 147
  19. 19.How many whole numbers lie between 6² and 7²?
  20. 20.A square garden has an area of 1521 square m. How long is each side (in m)?
  21. 21.What is 57²? =
  22. 22.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √1024? =
  24. 24.What is 14²? =
  25. 25.A square garden has an area of 144 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 891 must be divided to get a perfect square?
  27. 27.What is 71²? =
  28. 28.A square garden has an area of 3249 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 832 must be divided to get a perfect square?
  30. 30.What is √1600? =
  31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 18 must be divided to get a perfect square?
  33. 33.What is √6084? =
  34. 34.A square garden has an area of 196 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 36 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 39² and 40²?
  37. 37.What is 76²? =
  38. 38.What is 20²? =
  39. 39.Which of these is a perfect square? (a) 378 (b) 361 (c) 374
  40. 40.What is √2025? =

Answer key

  1. 70
  2. 169
  3. 10
  4. 32
  5. 13
  6. 33
  7. 36
  8. 31
  9. 441
  10. 1024
  11. 9
  12. 5625
  13. 86
  14. 80
  15. 24
  16. 90
  17. 70
  18. 144
  19. 12
  20. 39
  21. 3249
  22. 625
  23. 32
  24. 196
  25. 12
  26. 11
  27. 5041
  28. 57
  29. 13
  30. 40
  31. 46
  32. 2
  33. 78
  34. 14
  35. 6
  36. 78
  37. 5776
  38. 400
  39. 361
  40. 45

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