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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 719 · 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 55²? =
  2. 2.What is the smallest whole number by which 24 must be divided to get a perfect square?
  3. 3.How many whole numbers lie between 36² and 37²?
  4. 4.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 121 (b) 124 (c) 122
  6. 6.What is 29²? =
  7. 7.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 296 (b) 317 (c) 289
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 161 (b) 150 (c) 144
  11. 11.What is √4761? =
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 243 must be divided to get a perfect square?
  14. 14.What is 26²? =
  15. 15.What is the smallest whole number by which 56 must be divided to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 1342 (b) 1336 (c) 1296
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 28² and 29²?
  19. 19.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 41² and 42²?
  21. 21.Which of these is a perfect square? (a) 1022 (b) 995 (c) 961
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 15² and 16²?
  24. 24.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √1444? =
  26. 26.What is √7744? =
  27. 27.How many whole numbers lie between 30² and 31²?
  28. 28.What is √6241? =
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √9409? =
  33. 33.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  34. 34.What is √3721? =
  35. 35.What is 88²? =
  36. 36.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 2809 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 209 (b) 219 (c) 196
  39. 39.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 1620 (b) 1669 (c) 1600

Answer key

  1. 3025
  2. 6
  3. 72
  4. 3
  5. 121
  6. 841
  7. 14
  8. 289
  9. 361
  10. 144
  11. 69
  12. 576
  13. 3
  14. 676
  15. 14
  16. 1296
  17. 49
  18. 56
  19. 900
  20. 82
  21. 961
  22. 144
  23. 30
  24. 25
  25. 38
  26. 88
  27. 60
  28. 79
  29. 64
  30. 400
  31. 625
  32. 97
  33. 5
  34. 61
  35. 7744
  36. 6
  37. 53
  38. 196
  39. 7
  40. 1600

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