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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 65 · 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 85²? =
  2. 2.What is √2601? =
  3. 3.What is 31²? =
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 1000 (b) 971 (c) 961
  7. 7.What is 57²? =
  8. 8.A square garden has an area of 49 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 76²? =
  11. 11.What is the smallest whole number by which 810 must be divided to get a perfect square?
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 42² and 43²?
  14. 14.What is √196? =
  15. 15.What is 25²? =
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 512 (b) 498 (c) 484
  18. 18.How many whole numbers lie between 47² and 48²?
  19. 19.What is 32²? =
  20. 20.What is √2116? =
  21. 21.A square garden has an area of 2209 square m. How long is each side (in m)?
  22. 22.What is √144? =
  23. 23.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  24. 24.Which of these is a perfect square? (a) 214 (b) 196 (c) 200
  25. 25.How many whole numbers lie between 16² and 17²?
  26. 26.Which of these is a perfect square? (a) 152 (b) 154 (c) 144
  27. 27.Which of these is a perfect square? (a) 306 (b) 317 (c) 289
  28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
  29. 29.What is √6084? =
  30. 30.What is √8836? =
  31. 31.How many whole numbers lie between 27² and 28²?
  32. 32.Which of these is a perfect square? (a) 100 (b) 105 (c) 120
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √7225? =
  35. 35.What is 29²? =
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √5329? =
  38. 38.Which of these is a perfect square? (a) 173 (b) 169 (c) 172
  39. 39.What is √9025? =
  40. 40.What is 99²? =

Answer key

  1. 7225
  2. 51
  3. 961
  4. 196
  5. 25
  6. 961
  7. 3249
  8. 7
  9. 625
  10. 5776
  11. 10
  12. 49
  13. 84
  14. 14
  15. 625
  16. 441
  17. 484
  18. 94
  19. 1024
  20. 46
  21. 47
  22. 12
  23. 5
  24. 196
  25. 32
  26. 144
  27. 289
  28. 18
  29. 78
  30. 94
  31. 54
  32. 100
  33. 361
  34. 85
  35. 841
  36. 841
  37. 73
  38. 169
  39. 95
  40. 9801

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