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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 70 · 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 √3025? =
  2. 2.How many whole numbers lie between 21² and 22²?
  3. 3.Which of these is a perfect square? (a) 400 (b) 403 (c) 415
  4. 4.What is 19²? =
  5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 12² and 13²?
  7. 7.How many whole numbers lie between 13² and 14²?
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 23²? =
  10. 10.How many whole numbers lie between 46² and 47²?
  11. 11.What is the smallest whole number by which 325 must be divided to get a perfect square?
  12. 12.How many whole numbers lie between 38² and 39²?
  13. 13.What is √9025? =
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 7² and 8²?
  16. 16.Which of these is a perfect square? (a) 118 (b) 100 (c) 108
  17. 17.A square garden has an area of 289 square m. How long is each side (in m)?
  18. 18.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 192 must be divided to get a perfect square?
  20. 20.How many whole numbers lie between 32² and 33²?
  21. 21.What is 24²? =
  22. 22.What is 88²? =
  23. 23.What is √2401? =
  24. 24.What is 97²? =
  25. 25.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  26. 26.What is √5041? =
  27. 27.What is the smallest whole number by which 275 must be divided to get a perfect square?
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √2916? =
  30. 30.What is 75²? =
  31. 31.A square garden has an area of 36 square m. How long is each side (in m)?
  32. 32.What is 31²? =
  33. 33.What is √8100? =
  34. 34.Which of these is a perfect square? (a) 611 (b) 607 (c) 576
  35. 35.What is the smallest whole number by which 45 must be divided to get a perfect square?
  36. 36.Which of these is a perfect square? (a) 1225 (b) 1270 (c) 1229
  37. 37.What is 25²? =
  38. 38.What is the smallest whole number by which 60 must be divided to get a perfect square?
  39. 39.What is √7569? =
  40. 40.What is 29²? =

Answer key

  1. 55
  2. 42
  3. 400
  4. 361
  5. 324
  6. 24
  7. 26
  8. 49
  9. 529
  10. 92
  11. 13
  12. 76
  13. 95
  14. 47
  15. 14
  16. 100
  17. 17
  18. 6
  19. 3
  20. 64
  21. 576
  22. 7744
  23. 49
  24. 9409
  25. 15
  26. 71
  27. 11
  28. 676
  29. 54
  30. 5625
  31. 6
  32. 961
  33. 90
  34. 576
  35. 5
  36. 1225
  37. 625
  38. 15
  39. 87
  40. 841

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