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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 191 · 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.A square garden has an area of 484 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  3. 3.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  4. 4.What is the smallest whole number by which 20 must be divided to get a perfect square?
  5. 5.What is 97²? =
  6. 6.How many whole numbers lie between 6² and 7²?
  7. 7.What is 68²? =
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 8² and 9²?
  10. 10.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  11. 11.What is 77²? =
  12. 12.How many whole numbers lie between 18² and 19²?
  13. 13.What is √2916? =
  14. 14.What is 47²? =
  15. 15.What is 94²? =
  16. 16.A square garden has an area of 36 square m. How long is each side (in m)?
  17. 17.What is √169? =
  18. 18.What is √6724? =
  19. 19.A square garden has an area of 1681 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 29² and 30²?
  21. 21.How many whole numbers lie between 48² and 49²?
  22. 22.What is the smallest whole number by which 539 must be divided to get a perfect square?
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 56 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 441 (b) 453 (c) 469
  27. 27.How many whole numbers lie between 16² and 17²?
  28. 28.What is 25²? =
  29. 29.What is √484? =
  30. 30.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 12² and 13²?
  32. 32.What is 41²? =
  33. 33.How many whole numbers lie between 37² and 38²?
  34. 34.What is √361? =
  35. 35.What is 81²? =
  36. 36.What is 14²? =
  37. 37.What is √1849? =
  38. 38.How many whole numbers lie between 39² and 40²?
  39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 36² and 37²?

Answer key

  1. 22
  2. 7
  3. 14
  4. 5
  5. 9409
  6. 12
  7. 4624
  8. 144
  9. 16
  10. 6
  11. 5929
  12. 36
  13. 54
  14. 2209
  15. 8836
  16. 6
  17. 13
  18. 82
  19. 41
  20. 58
  21. 96
  22. 11
  23. 100
  24. 441
  25. 14
  26. 441
  27. 32
  28. 625
  29. 22
  30. 14
  31. 24
  32. 1681
  33. 74
  34. 19
  35. 6561
  36. 196
  37. 43
  38. 78
  39. 81
  40. 72

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