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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 98 · 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 12 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √3481? =
  4. 4.What is 83²? =
  5. 5.Which of these is a perfect square? (a) 511 (b) 484 (c) 512
  6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 256 square m. How long is each side (in m)?
  10. 10.What is 74²? =
  11. 11.What is 64²? =
  12. 12.What is √3844? =
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  14. 14.A square garden has an area of 324 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 18 must be divided to get a perfect square?
  16. 16.A square garden has an area of 729 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 1359 (b) 1296 (c) 1323
  18. 18.How many whole numbers lie between 38² and 39²?
  19. 19.What is √441? =
  20. 20.What is the smallest whole number by which 12 must be divided to get a perfect square?
  21. 21.How many whole numbers lie between 9² and 10²?
  22. 22.A square garden has an area of 3364 square m. How long is each side (in m)?
  23. 23.What is √2809? =
  24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 41² and 42²?
  26. 26.What is 88²? =
  27. 27.What is the smallest whole number by which 125 must be divided to get a perfect square?
  28. 28.What is the smallest whole number by which 40 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 42² and 43²?
  30. 30.Which of these is a perfect square? (a) 820 (b) 784 (c) 805
  31. 31.How many whole numbers lie between 19² and 20²?
  32. 32.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  33. 33.What is √225? =
  34. 34.What is 87²? =
  35. 35.Which of these is a perfect square? (a) 100 (b) 103 (c) 101
  36. 36.What is the smallest whole number by which 108 must be divided to get a perfect square?
  37. 37.How many whole numbers lie between 36² and 37²?
  38. 38.How many whole numbers lie between 28² and 29²?
  39. 39.Which of these is a perfect square? (a) 1031 (b) 1024 (c) 1035
  40. 40.How many whole numbers lie between 24² and 25²?

Answer key

  1. 144
  2. 289
  3. 59
  4. 6889
  5. 484
  6. 324
  7. 3
  8. 676
  9. 16
  10. 5476
  11. 4096
  12. 62
  13. 64
  14. 18
  15. 2
  16. 27
  17. 1296
  18. 76
  19. 21
  20. 3
  21. 18
  22. 58
  23. 53
  24. 169
  25. 82
  26. 7744
  27. 5
  28. 10
  29. 84
  30. 784
  31. 38
  32. 7
  33. 15
  34. 7569
  35. 100
  36. 3
  37. 72
  38. 56
  39. 1024
  40. 48

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