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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 643 · 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 14 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 25 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 1849 square m. How long is each side (in m)?
  4. 4.What is 80²? =
  5. 5.What is √5625? =
  6. 6.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  7. 7.What is √5041? =
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 69²? =
  10. 10.A square garden has an area of 2704 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 33² and 34²?
  12. 12.How many whole numbers lie between 18² and 19²?
  13. 13.What is 76²? =
  14. 14.How many whole numbers lie between 8² and 9²?
  15. 15.Which of these is a perfect square? (a) 729 (b) 759 (c) 742
  16. 16.What is 51²? =
  17. 17.What is √3025? =
  18. 18.What is 44²? =
  19. 19.What is the smallest whole number by which 216 must be divided to get a perfect square?
  20. 20.What is √1296? =
  21. 21.What is 62²? =
  22. 22.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  24. 24.What is 14²? =
  25. 25.How many whole numbers lie between 24² and 25²?
  26. 26.What is the smallest whole number by which 52 must be divided to get a perfect square?
  27. 27.What is the smallest whole number by which 252 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 28² and 29²?
  29. 29.What is 43²? =
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  32. 32.How many whole numbers lie between 19² and 20²?
  33. 33.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  34. 34.A square garden has an area of 2116 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 9² and 10²?
  36. 36.How many whole numbers lie between 17² and 18²?
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is 50²? =
  39. 39.What is the smallest whole number by which 150 must be divided to get a perfect square?
  40. 40.A square garden has an area of 225 square m. How long is each side (in m)?

Answer key

  1. 196
  2. 5
  3. 43
  4. 6400
  5. 75
  6. 14
  7. 71
  8. 676
  9. 4761
  10. 52
  11. 66
  12. 36
  13. 5776
  14. 16
  15. 729
  16. 2601
  17. 55
  18. 1936
  19. 6
  20. 36
  21. 3844
  22. 7
  23. 15
  24. 196
  25. 48
  26. 13
  27. 7
  28. 56
  29. 1849
  30. 900
  31. 6
  32. 38
  33. 15
  34. 46
  35. 18
  36. 34
  37. 256
  38. 2500
  39. 6
  40. 15

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