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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 683 · 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 √961? =
  2. 2.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 333 (b) 324 (c) 339
  4. 4.What is the smallest whole number by which 50 must be divided to get a perfect square?
  5. 5.A square garden has an area of 841 square m. How long is each side (in m)?
  6. 6.What is 52²? =
  7. 7.A square garden has an area of 3025 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 961 square m. How long is each side (in m)?
  9. 9.A square garden has an area of 3364 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 1600 square m. How long is each side (in m)?
  11. 11.What is √3600? =
  12. 12.A square garden has an area of 1936 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 44 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 731 (b) 733 (c) 729
  15. 15.Which of these is a perfect square? (a) 202 (b) 196 (c) 201
  16. 16.A square garden has an area of 2809 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 2601 square m. How long is each side (in m)?
  18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 290 (b) 289 (c) 298
  21. 21.What is the smallest whole number by which 294 must be divided to get a perfect square?
  22. 22.What is √7744? =
  23. 23.How many whole numbers lie between 47² and 48²?
  24. 24.What is 99²? =
  25. 25.What is 73²? =
  26. 26.What is the smallest whole number by which 147 must be divided to get a perfect square?
  27. 27.What is 28²? =
  28. 28.What is 91²? =
  29. 29.Which of these is a perfect square? (a) 477 (b) 475 (c) 441
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  32. 32.How many whole numbers lie between 39² and 40²?
  33. 33.What is √9025? =
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 196 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 21² and 22²?
  38. 38.What is √9604? =
  39. 39.How many whole numbers lie between 19² and 20²?
  40. 40.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 31
  2. 441
  3. 324
  4. 2
  5. 29
  6. 2704
  7. 55
  8. 31
  9. 58
  10. 40
  11. 60
  12. 44
  13. 11
  14. 729
  15. 196
  16. 53
  17. 51
  18. 121
  19. 49
  20. 289
  21. 6
  22. 88
  23. 94
  24. 9801
  25. 5329
  26. 3
  27. 784
  28. 8281
  29. 441
  30. 841
  31. 5
  32. 78
  33. 95
  34. 36
  35. 14
  36. 144
  37. 42
  38. 98
  39. 38
  40. 196

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