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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 64 · 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 23² and 24²?
  2. 2.What is √324? =
  3. 3.A square garden has an area of 3364 square m. How long is each side (in m)?
  4. 4.What is √1369? =
  5. 5.How many whole numbers lie between 32² and 33²?
  6. 6.What is the smallest whole number by which 75 must be divided to get a perfect square?
  7. 7.How many whole numbers lie between 50² and 51²?
  8. 8.A square garden has an area of 169 square m. How long is each side (in m)?
  9. 9.What is √6241? =
  10. 10.What is √2809? =
  11. 11.Which of these is a perfect square? (a) 1177 (b) 1156 (c) 1173
  12. 12.Which of these is a perfect square? (a) 408 (b) 400 (c) 404
  13. 13.How many whole numbers lie between 5² and 6²?
  14. 14.What is 24²? =
  15. 15.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 1936 square m. How long is each side (in m)?
  18. 18.What is 89²? =
  19. 19.What is √1521? =
  20. 20.What is √1156? =
  21. 21.How many whole numbers lie between 18² and 19²?
  22. 22.What is 79²? =
  23. 23.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 484 (b) 509 (c) 496
  26. 26.What is 36²? =
  27. 27.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √9604? =
  30. 30.What is √1024? =
  31. 31.What is 93²? =
  32. 32.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  33. 33.A square garden has an area of 289 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √6889? =
  36. 36.Which of these is a perfect square? (a) 1521 (b) 1588 (c) 1553
  37. 37.A square garden has an area of 2304 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 28² and 29²?
  39. 39.What is √5929? =
  40. 40.What is 34²? =

Answer key

  1. 46
  2. 18
  3. 58
  4. 37
  5. 64
  6. 3
  7. 100
  8. 13
  9. 79
  10. 53
  11. 1156
  12. 400
  13. 10
  14. 576
  15. 15
  16. 361
  17. 44
  18. 7921
  19. 39
  20. 34
  21. 36
  22. 6241
  23. 6
  24. 36
  25. 484
  26. 1296
  27. 13
  28. 100
  29. 98
  30. 32
  31. 8649
  32. 900
  33. 17
  34. 81
  35. 83
  36. 1521
  37. 48
  38. 56
  39. 77
  40. 1156

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