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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 74 · 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 26²? =
  2. 2.Which of these is a perfect square? (a) 1310 (b) 1331 (c) 1296
  3. 3.A square garden has an area of 2401 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 3600 square m. How long is each side (in m)?
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √5329? =
  7. 7.What is 70²? =
  8. 8.What is 76²? =
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 361 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 35² and 36²?
  14. 14.What is √1156? =
  15. 15.What is √7569? =
  16. 16.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  17. 17.What is √9025? =
  18. 18.How many whole numbers lie between 10² and 11²?
  19. 19.Which of these is a perfect square? (a) 528 (b) 484 (c) 517
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 43² and 44²?
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 106 (b) 115 (c) 100
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  28. 28.Which of these is a perfect square? (a) 1225 (b) 1255 (c) 1288
  29. 29.What is 99²? =
  30. 30.Which of these is a perfect square? (a) 919 (b) 900 (c) 903
  31. 31.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  32. 32.What is √4096? =
  33. 33.A square garden has an area of 196 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 1024 (b) 1061 (c) 1081
  37. 37.How many whole numbers lie between 40² and 41²?
  38. 38.How many whole numbers lie between 15² and 16²?
  39. 39.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  40. 40.What is 32²? =

Answer key

  1. 676
  2. 1296
  3. 49
  4. 60
  5. 25
  6. 73
  7. 4900
  8. 5776
  9. 256
  10. 676
  11. 19
  12. 625
  13. 70
  14. 34
  15. 87
  16. 3
  17. 95
  18. 20
  19. 484
  20. 100
  21. 14
  22. 400
  23. 86
  24. 36
  25. 11
  26. 100
  27. 144
  28. 1225
  29. 9801
  30. 900
  31. 14
  32. 64
  33. 14
  34. 2
  35. 900
  36. 1024
  37. 80
  38. 30
  39. 11
  40. 1024

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