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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 401 · 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 √1156? =
  2. 2.What is √625? =
  3. 3.How many whole numbers lie between 18² and 19²?
  4. 4.What is 22²? =
  5. 5.A square garden has an area of 2116 square m. How long is each side (in m)?
  6. 6.What is √7225? =
  7. 7.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  8. 8.What is 30²? =
  9. 9.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 676 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 625 square m. How long is each side (in m)?
  12. 12.Which of these is a perfect square? (a) 311 (b) 289 (c) 310
  13. 13.Which of these is a perfect square? (a) 169 (b) 194 (c) 177
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 14² and 15²?
  16. 16.Which of these is a perfect square? (a) 895 (b) 841 (c) 886
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √9409? =
  19. 19.What is 31²? =
  20. 20.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is 51²? =
  22. 22.How many whole numbers lie between 43² and 44²?
  23. 23.What is 67²? =
  24. 24.How many whole numbers lie between 11² and 12²?
  25. 25.What is √2916? =
  26. 26.What is √784? =
  27. 27.Which of these is a perfect square? (a) 112 (b) 105 (c) 100
  28. 28.A square garden has an area of 2304 square m. How long is each side (in m)?
  29. 29.What is 82²? =
  30. 30.What is the smallest whole number by which 48 must be divided to get a perfect square?
  31. 31.What is √8464? =
  32. 32.What is √4489? =
  33. 33.What is √121? =
  34. 34.What is the smallest whole number by which 90 must be divided to get a perfect square?
  35. 35.What is √7744? =
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √5929? =
  38. 38.Which of these is a perfect square? (a) 1156 (b) 1202 (c) 1198
  39. 39.What is the smallest whole number by which 150 must be divided to get a perfect square?
  40. 40.What is √1600? =

Answer key

  1. 34
  2. 25
  3. 36
  4. 484
  5. 46
  6. 85
  7. 15
  8. 900
  9. 7
  10. 26
  11. 25
  12. 289
  13. 169
  14. 784
  15. 28
  16. 841
  17. 81
  18. 97
  19. 961
  20. 256
  21. 2601
  22. 86
  23. 4489
  24. 22
  25. 54
  26. 28
  27. 100
  28. 48
  29. 6724
  30. 3
  31. 92
  32. 67
  33. 11
  34. 10
  35. 88
  36. 289
  37. 77
  38. 1156
  39. 6
  40. 40

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