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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 729 · 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 √289? =
  2. 2.Which of these is a perfect square? (a) 841 (b) 868 (c) 886
  3. 3.Which of these is a perfect square? (a) 1514 (b) 1444 (c) 1519
  4. 4.What is 16²? =
  5. 5.What is 73²? =
  6. 6.How many whole numbers lie between 47² and 48²?
  7. 7.What is 72²? =
  8. 8.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  9. 9.What is √8281? =
  10. 10.Which of these is a perfect square? (a) 1220 (b) 1193 (c) 1156
  11. 11.What is √5625? =
  12. 12.Which of these is a perfect square? (a) 615 (b) 594 (c) 576
  13. 13.How many whole numbers lie between 18² and 19²?
  14. 14.What is 98²? =
  15. 15.Which of these is a perfect square? (a) 625 (b) 649 (c) 631
  16. 16.What is √961? =
  17. 17.What is the smallest whole number by which 240 must be divided to get a perfect square?
  18. 18.What is √625? =
  19. 19.What is √1521? =
  20. 20.A square garden has an area of 36 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 1240 (b) 1225 (c) 1269
  22. 22.What is √484? =
  23. 23.A square garden has an area of 64 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 24² and 25²?
  27. 27.A square garden has an area of 400 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 121 square m. How long is each side (in m)?
  30. 30.What is 55²? =
  31. 31.Which of these is a perfect square? (a) 987 (b) 961 (c) 977
  32. 32.What is √6561? =
  33. 33.What is 94²? =
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  36. 36.A square garden has an area of 2704 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 230 (b) 225 (c) 238
  38. 38.Which of these is a perfect square? (a) 693 (b) 700 (c) 676
  39. 39.What is the smallest whole number by which 125 must be divided to get a perfect square?
  40. 40.What is 51²? =

Answer key

  1. 17
  2. 841
  3. 1444
  4. 256
  5. 5329
  6. 94
  7. 5184
  8. 2
  9. 91
  10. 1156
  11. 75
  12. 576
  13. 36
  14. 9604
  15. 625
  16. 31
  17. 15
  18. 25
  19. 39
  20. 6
  21. 1225
  22. 22
  23. 8
  24. 13
  25. 100
  26. 48
  27. 20
  28. 121
  29. 11
  30. 3025
  31. 961
  32. 81
  33. 8836
  34. 81
  35. 225
  36. 52
  37. 225
  38. 676
  39. 5
  40. 2601

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