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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 214 · 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 2025 square m. How long is each side (in m)?
  2. 2.What is 61²? =
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √225? =
  5. 5.What is √6241? =
  6. 6.How many whole numbers lie between 26² and 27²?
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 18² and 19²?
  9. 9.What is 25²? =
  10. 10.Which of these is a perfect square? (a) 196 (b) 208 (c) 223
  11. 11.What is √729? =
  12. 12.What is the smallest whole number by which 162 must be divided to get a perfect square?
  13. 13.How many whole numbers lie between 49² and 50²?
  14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 44²? =
  16. 16.What is √961? =
  17. 17.What is √169? =
  18. 18.What is 46²? =
  19. 19.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  20. 20.What is the smallest whole number by which 48 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 416 (b) 400 (c) 439
  22. 22.How many whole numbers lie between 50² and 51²?
  23. 23.What is the smallest whole number by which 325 must be divided to get a perfect square?
  24. 24.What is 81²? =
  25. 25.A square garden has an area of 2916 square m. How long is each side (in m)?
  26. 26.What is 38²? =
  27. 27.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 25² and 26²?
  30. 30.Which of these is a perfect square? (a) 900 (b) 924 (c) 910
  31. 31.How many whole numbers lie between 9² and 10²?
  32. 32.How many whole numbers lie between 6² and 7²?
  33. 33.What is the smallest whole number by which 294 must be divided to get a perfect square?
  34. 34.What is √6724? =
  35. 35.What is √5184? =
  36. 36.What is 47²? =
  37. 37.What is √7744? =
  38. 38.What is √8649? =
  39. 39.A square garden has an area of 1089 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 126 must be multiplied to get a perfect square?

Answer key

  1. 45
  2. 3721
  3. 196
  4. 15
  5. 79
  6. 52
  7. 400
  8. 36
  9. 625
  10. 196
  11. 27
  12. 2
  13. 98
  14. 49
  15. 1936
  16. 31
  17. 13
  18. 2116
  19. 14
  20. 3
  21. 400
  22. 100
  23. 13
  24. 6561
  25. 54
  26. 1444
  27. 289
  28. 625
  29. 50
  30. 900
  31. 18
  32. 12
  33. 6
  34. 82
  35. 72
  36. 2209
  37. 88
  38. 93
  39. 33
  40. 14

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