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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 371 · 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.How many whole numbers lie between 17² and 18²?
  2. 2.Which of these is a perfect square? (a) 839 (b) 784 (c) 812
  3. 3.A square garden has an area of 1521 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 694 (b) 718 (c) 676
  5. 5.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √1296? =
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  9. 9.What is 71²? =
  10. 10.Which of these is a perfect square? (a) 185 (b) 169 (c) 180
  11. 11.A square garden has an area of 1296 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 1156 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √961? =
  15. 15.What is √4624? =
  16. 16.Which of these is a perfect square? (a) 588 (b) 577 (c) 576
  17. 17.What is 42²? =
  18. 18.Which of these is a perfect square? (a) 300 (b) 308 (c) 289
  19. 19.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  20. 20.How many whole numbers lie between 44² and 45²?
  21. 21.Which of these is a perfect square? (a) 1256 (b) 1257 (c) 1225
  22. 22.What is 24²? =
  23. 23.How many whole numbers lie between 39² and 40²?
  24. 24.What is 16²? =
  25. 25.What is 82²? =
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 23² and 24²?
  28. 28.What is the smallest whole number by which 832 must be divided to get a perfect square?
  29. 29.What is the smallest whole number by which 250 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 20 must be divided to get a perfect square?
  31. 31.What is 90²? =
  32. 32.What is 83²? =
  33. 33.How many whole numbers lie between 15² and 16²?
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 433 (b) 400 (c) 415
  37. 37.What is 73²? =
  38. 38.What is √1764? =
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 48² and 49²?

Answer key

  1. 34
  2. 784
  3. 39
  4. 676
  5. 225
  6. 36
  7. 49
  8. 7
  9. 5041
  10. 169
  11. 36
  12. 34
  13. 289
  14. 31
  15. 68
  16. 576
  17. 1764
  18. 289
  19. 15
  20. 88
  21. 1225
  22. 576
  23. 78
  24. 256
  25. 6724
  26. 256
  27. 46
  28. 13
  29. 10
  30. 5
  31. 8100
  32. 6889
  33. 30
  34. 25
  35. 441
  36. 400
  37. 5329
  38. 42
  39. 676
  40. 96

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