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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 134 · 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 √144? =
  2. 2.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 737 (b) 756 (c) 729
  4. 4.A square garden has an area of 196 square m. How long is each side (in m)?
  5. 5.What is 65²? =
  6. 6.How many whole numbers lie between 35² and 36²?
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.What is √7396? =
  9. 9.A square garden has an area of 25 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √3364? =
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 504 must be divided to get a perfect square?
  16. 16.What is 48²? =
  17. 17.Which of these is a perfect square? (a) 114 (b) 100 (c) 112
  18. 18.A square garden has an area of 3136 square m. How long is each side (in m)?
  19. 19.What is 90²? =
  20. 20.A square garden has an area of 625 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 98 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1533 (b) 1598 (c) 1521
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 10² and 11²?
  25. 25.A square garden has an area of 400 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 19²? =
  28. 28.How many whole numbers lie between 47² and 48²?
  29. 29.What is 83²? =
  30. 30.A square garden has an area of 49 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 8² and 9²?
  32. 32.What is √4761? =
  33. 33.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  34. 34.Which of these is a perfect square? (a) 790 (b) 807 (c) 784
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 43²? =
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 28 must be multiplied to get a perfect square?

Answer key

  1. 12
  2. 13
  3. 729
  4. 14
  5. 4225
  6. 70
  7. 9
  8. 86
  9. 5
  10. 11
  11. 676
  12. 841
  13. 58
  14. 100
  15. 14
  16. 2304
  17. 100
  18. 56
  19. 8100
  20. 25
  21. 2
  22. 1521
  23. 529
  24. 20
  25. 20
  26. 784
  27. 361
  28. 94
  29. 6889
  30. 7
  31. 16
  32. 69
  33. 36
  34. 784
  35. 441
  36. 1849
  37. 256
  38. 400
  39. 10
  40. 7

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