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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 130 · 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) 226 (b) 225 (c) 229
  3. 3.How many whole numbers lie between 12² and 13²?
  4. 4.How many whole numbers lie between 33² and 34²?
  5. 5.What is √9216? =
  6. 6.What is 96²? =
  7. 7.A square garden has an area of 400 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 1369 (b) 1427 (c) 1410
  9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 1024 (b) 1072 (c) 1076
  11. 11.A square garden has an area of 1764 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 529 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  14. 14.A square garden has an area of 2025 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  16. 16.What is 22²? =
  17. 17.What is √8100? =
  18. 18.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 54 must be divided to get a perfect square?
  20. 20.What is √7921? =
  21. 21.How many whole numbers lie between 17² and 18²?
  22. 22.What is 33²? =
  23. 23.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  24. 24.What is √3600? =
  25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 64²? =
  27. 27.What is 72²? =
  28. 28.How many whole numbers lie between 7² and 8²?
  29. 29.How many whole numbers lie between 19² and 20²?
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  31. 31.A square garden has an area of 169 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 128 (b) 137 (c) 121
  33. 33.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  34. 34.What is 50²? =
  35. 35.How many whole numbers lie between 36² and 37²?
  36. 36.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  37. 37.What is 57²? =
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 7
  2. 225
  3. 24
  4. 66
  5. 96
  6. 9216
  7. 20
  8. 1369
  9. 12
  10. 1024
  11. 42
  12. 23
  13. 10
  14. 45
  15. 15
  16. 484
  17. 90
  18. 5
  19. 6
  20. 89
  21. 34
  22. 1089
  23. 14
  24. 60
  25. 144
  26. 4096
  27. 5184
  28. 14
  29. 38
  30. 64
  31. 13
  32. 121
  33. 11
  34. 2500
  35. 72
  36. 7
  37. 3249
  38. 25
  39. 49
  40. 100

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