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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 677 · 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.Which of these is a perfect square? (a) 1571 (b) 1521 (c) 1579
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √7744? =
  4. 4.What is 31²? =
  5. 5.What is 21²? =
  6. 6.What is 35²? =
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  9. 9.A square garden has an area of 2401 square m. How long is each side (in m)?
  10. 10.What is 32²? =
  11. 11.Which of these is a perfect square? (a) 1677 (b) 1600 (c) 1653
  12. 12.A square garden has an area of 676 square m. How long is each side (in m)?
  13. 13.What is √9216? =
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 50² and 51²?
  16. 16.What is √7921? =
  17. 17.What is √6241? =
  18. 18.A square garden has an area of 81 square m. How long is each side (in m)?
  19. 19.What is 14²? =
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 169 (b) 190 (c) 174
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 25 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 14² and 15²?
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 97²? =
  28. 28.How many whole numbers lie between 11² and 12²?
  29. 29.What is the smallest whole number by which 32 must be divided to get a perfect square?
  30. 30.What is 46²? =
  31. 31.Which of these is a perfect square? (a) 361 (b) 385 (c) 362
  32. 32.How many whole numbers lie between 36² and 37²?
  33. 33.What is 44²? =
  34. 34.How many whole numbers lie between 40² and 41²?
  35. 35.How many whole numbers lie between 29² and 30²?
  36. 36.What is √1764? =
  37. 37.Which of these is a perfect square? (a) 225 (b) 255 (c) 246
  38. 38.What is 66²? =
  39. 39.What is 23²? =
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 1521
  2. 100
  3. 88
  4. 961
  5. 441
  6. 1225
  7. 441
  8. 11
  9. 49
  10. 1024
  11. 1600
  12. 26
  13. 96
  14. 289
  15. 100
  16. 89
  17. 79
  18. 9
  19. 196
  20. 784
  21. 169
  22. 400
  23. 529
  24. 5
  25. 28
  26. 841
  27. 9409
  28. 22
  29. 2
  30. 2116
  31. 361
  32. 72
  33. 1936
  34. 80
  35. 58
  36. 42
  37. 225
  38. 4356
  39. 529
  40. 36

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