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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 373 · 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 the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is 41²? =
  3. 3.What is √529? =
  4. 4.How many whole numbers lie between 36² and 37²?
  5. 5.What is √6724? =
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √7921? =
  8. 8.Which of these is a perfect square? (a) 290 (b) 289 (c) 306
  9. 9.What is 38²? =
  10. 10.Which of these is a perfect square? (a) 124 (b) 121 (c) 125
  11. 11.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 225 (b) 238 (c) 241
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 48²? =
  15. 15.Which of these is a perfect square? (a) 1600 (b) 1623 (c) 1637
  16. 16.What is 78²? =
  17. 17.What is √4489? =
  18. 18.What is 14²? =
  19. 19.What is √324? =
  20. 20.What is 69²? =
  21. 21.What is √6561? =
  22. 22.What is 64²? =
  23. 23.What is √8836? =
  24. 24.How many whole numbers lie between 43² and 44²?
  25. 25.What is the smallest whole number by which 704 must be divided to get a perfect square?
  26. 26.What is 25²? =
  27. 27.A square garden has an area of 484 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the smallest whole number by which 208 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 637 must be divided to get a perfect square?
  31. 31.A square garden has an area of 625 square m. How long is each side (in m)?
  32. 32.What is √3600? =
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 12²? =
  35. 35.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  36. 36.What is √6084? =
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 46² and 47²?
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 41² and 42²?

Answer key

  1. 100
  2. 1681
  3. 23
  4. 72
  5. 82
  6. 64
  7. 89
  8. 289
  9. 1444
  10. 121
  11. 5
  12. 225
  13. 25
  14. 2304
  15. 1600
  16. 6084
  17. 67
  18. 196
  19. 18
  20. 4761
  21. 81
  22. 4096
  23. 94
  24. 86
  25. 11
  26. 625
  27. 22
  28. 36
  29. 13
  30. 13
  31. 25
  32. 60
  33. 121
  34. 144
  35. 14
  36. 78
  37. 289
  38. 92
  39. 529
  40. 82

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