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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 657 · 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.How many whole numbers lie between 24² and 25²?
  2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 640 must be divided to get a perfect square?
  4. 4.What is 12²? =
  5. 5.What is √841? =
  6. 6.What is the smallest whole number by which 18 must be divided to get a perfect square?
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 94²? =
  9. 9.A square garden has an area of 324 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 2209 square m. How long is each side (in m)?
  11. 11.What is 80²? =
  12. 12.Which of these is a perfect square? (a) 143 (b) 141 (c) 121
  13. 13.What is √7744? =
  14. 14.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  15. 15.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  16. 16.What is 78²? =
  17. 17.What is √7396? =
  18. 18.Which of these is a perfect square? (a) 772 (b) 770 (c) 729
  19. 19.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 34² and 35²?
  21. 21.What is √256? =
  22. 22.What is 56²? =
  23. 23.What is √2025? =
  24. 24.What is the smallest whole number by which 294 must be divided to get a perfect square?
  25. 25.How many whole numbers lie between 28² and 29²?
  26. 26.What is 62²? =
  27. 27.How many whole numbers lie between 42² and 43²?
  28. 28.A square garden has an area of 529 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √400? =
  31. 31.What is 58²? =
  32. 32.Which of these is a perfect square? (a) 625 (b) 669 (c) 638
  33. 33.What is √1521? =
  34. 34.How many whole numbers lie between 45² and 46²?
  35. 35.What is 99²? =
  36. 36.What is √4225? =
  37. 37.What is the smallest whole number by which 180 must be divided to get a perfect square?
  38. 38.What is 22²? =
  39. 39.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 9² and 10²?

Answer key

  1. 48
  2. 576
  3. 10
  4. 144
  5. 29
  6. 2
  7. 900
  8. 8836
  9. 18
  10. 47
  11. 6400
  12. 121
  13. 88
  14. 14
  15. 13
  16. 6084
  17. 86
  18. 729
  19. 13
  20. 68
  21. 16
  22. 3136
  23. 45
  24. 6
  25. 56
  26. 3844
  27. 84
  28. 23
  29. 196
  30. 20
  31. 3364
  32. 625
  33. 39
  34. 90
  35. 9801
  36. 65
  37. 5
  38. 484
  39. 10
  40. 18

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