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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 298 · 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.What is √144? =
  2. 2.How many whole numbers lie between 19² and 20²?
  3. 3.What is 65²? =
  4. 4.What is 71²? =
  5. 5.A square garden has an area of 841 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 1156 (b) 1162 (c) 1176
  7. 7.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  8. 8.What is 29²? =
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 40² and 41²?
  12. 12.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  13. 13.What is √6889? =
  14. 14.What is √1089? =
  15. 15.How many whole numbers lie between 36² and 37²?
  16. 16.What is √1936? =
  17. 17.Which of these is a perfect square? (a) 784 (b) 791 (c) 838
  18. 18.What is 72²? =
  19. 19.Which of these is a perfect square? (a) 777 (b) 772 (c) 729
  20. 20.Which of these is a perfect square? (a) 964 (b) 968 (c) 961
  21. 21.What is √1024? =
  22. 22.What is 38²? =
  23. 23.Which of these is a perfect square? (a) 182 (b) 181 (c) 169
  24. 24.Which of these is a perfect square? (a) 225 (b) 232 (c) 227
  25. 25.A square garden has an area of 1681 square m. How long is each side (in m)?
  26. 26.What is √3721? =
  27. 27.A square garden has an area of 3136 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 275 must be divided to get a perfect square?
  29. 29.A square garden has an area of 100 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 1409 (b) 1382 (c) 1369
  32. 32.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  33. 33.What is 86²? =
  34. 34.A square garden has an area of 900 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  36. 36.A square garden has an area of 225 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 25² and 26²?
  38. 38.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  39. 39.How many whole numbers lie between 10² and 11²?
  40. 40.How many whole numbers lie between 46² and 47²?

Answer key

  1. 12
  2. 38
  3. 4225
  4. 5041
  5. 29
  6. 1156
  7. 2
  8. 841
  9. 400
  10. 225
  11. 80
  12. 2
  13. 83
  14. 33
  15. 72
  16. 44
  17. 784
  18. 5184
  19. 729
  20. 961
  21. 32
  22. 1444
  23. 169
  24. 225
  25. 41
  26. 61
  27. 56
  28. 11
  29. 10
  30. 2
  31. 1369
  32. 5
  33. 7396
  34. 30
  35. 676
  36. 15
  37. 50
  38. 3
  39. 20
  40. 92

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