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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 642 · 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) 663 (b) 625 (c) 630
  2. 2.How many whole numbers lie between 48² and 49²?
  3. 3.What is 25²? =
  4. 4.What is √961? =
  5. 5.A square garden has an area of 64 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 25² and 26²?
  7. 7.How many whole numbers lie between 41² and 42²?
  8. 8.How many whole numbers lie between 8² and 9²?
  9. 9.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 1130 (b) 1100 (c) 1089
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 144 (b) 166 (c) 156
  15. 15.How many whole numbers lie between 31² and 32²?
  16. 16.A square garden has an area of 361 square m. How long is each side (in m)?
  17. 17.What is 80²? =
  18. 18.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  19. 19.A square garden has an area of 2916 square m. How long is each side (in m)?
  20. 20.A square garden has an area of 100 square m. How long is each side (in m)?
  21. 21.What is √196? =
  22. 22.A square garden has an area of 1764 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 240 must be divided to get a perfect square?
  24. 24.How many whole numbers lie between 37² and 38²?
  25. 25.Which of these is a perfect square? (a) 196 (b) 206 (c) 216
  26. 26.What is √3721? =
  27. 27.Which of these is a perfect square? (a) 285 (b) 274 (c) 256
  28. 28.Which of these is a perfect square? (a) 134 (b) 121 (c) 122
  29. 29.A square garden has an area of 81 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 2500 square m. How long is each side (in m)?
  31. 31.What is √6889? =
  32. 32.What is 59²? =
  33. 33.What is the smallest whole number by which 162 must be divided to get a perfect square?
  34. 34.A square garden has an area of 25 square m. How long is each side (in m)?
  35. 35.What is 34²? =
  36. 36.A square garden has an area of 1681 square m. How long is each side (in m)?
  37. 37.What is 26²? =
  38. 38.What is 24²? =
  39. 39.Which of these is a perfect square? (a) 616 (b) 576 (c) 619
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 625
  2. 96
  3. 625
  4. 31
  5. 8
  6. 50
  7. 82
  8. 16
  9. 6
  10. 49
  11. 13
  12. 1089
  13. 841
  14. 144
  15. 62
  16. 19
  17. 6400
  18. 10
  19. 54
  20. 10
  21. 14
  22. 42
  23. 15
  24. 74
  25. 196
  26. 61
  27. 256
  28. 121
  29. 9
  30. 50
  31. 83
  32. 3481
  33. 2
  34. 5
  35. 1156
  36. 41
  37. 676
  38. 576
  39. 576
  40. 100

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