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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 419 · 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 15² and 16²?
  2. 2.What is 35²? =
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 23² and 24²?
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √5329? =
  7. 7.What is √1444? =
  8. 8.Which of these is a perfect square? (a) 1680 (b) 1600 (c) 1657
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 48²? =
  12. 12.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  13. 13.A square garden has an area of 625 square m. How long is each side (in m)?
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 24² and 25²?
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 49² and 50²?
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 167 (b) 144 (c) 146
  20. 20.What is the smallest whole number by which 343 must be divided to get a perfect square?
  21. 21.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √1849? =
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 87²? =
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √3025? =
  27. 27.What is 55²? =
  28. 28.A square garden has an area of 121 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 35² and 36²?
  30. 30.How many whole numbers lie between 11² and 12²?
  31. 31.Which of these is a perfect square? (a) 671 (b) 662 (c) 625
  32. 32.What is √2025? =
  33. 33.Which of these is a perfect square? (a) 251 (b) 225 (c) 246
  34. 34.A square garden has an area of 1369 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 90²? =
  37. 37.What is 92²? =
  38. 38.What is the smallest whole number by which 98 must be divided to get a perfect square?
  39. 39.What is 79²? =
  40. 40.What is √1681? =

Answer key

  1. 30
  2. 1225
  3. 441
  4. 46
  5. 49
  6. 73
  7. 38
  8. 1600
  9. 144
  10. 169
  11. 2304
  12. 3
  13. 25
  14. 81
  15. 48
  16. 25
  17. 98
  18. 289
  19. 144
  20. 7
  21. 900
  22. 43
  23. 121
  24. 7569
  25. 361
  26. 55
  27. 3025
  28. 11
  29. 70
  30. 22
  31. 625
  32. 45
  33. 225
  34. 37
  35. 400
  36. 8100
  37. 8464
  38. 2
  39. 6241
  40. 41

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