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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 188 · 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 √3969? =
  2. 2.How many whole numbers lie between 18² and 19²?
  3. 3.A square garden has an area of 961 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 625 square m. How long is each side (in m)?
  5. 5.What is 26²? =
  6. 6.What is 19²? =
  7. 7.What is the smallest whole number by which 40 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 250 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 26² and 27²?
  10. 10.A square garden has an area of 3249 square m. How long is each side (in m)?
  11. 11.What is 93²? =
  12. 12.How many whole numbers lie between 30² and 31²?
  13. 13.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  14. 14.What is √961? =
  15. 15.A square garden has an area of 2601 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 38² and 39²?
  17. 17.Which of these is a perfect square? (a) 196 (b) 209 (c) 212
  18. 18.A square garden has an area of 256 square m. How long is each side (in m)?
  19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 34²? =
  21. 21.What is 57²? =
  22. 22.What is √7225? =
  23. 23.What is 74²? =
  24. 24.Which of these is a perfect square? (a) 132 (b) 121 (c) 124
  25. 25.What is the smallest whole number by which 63 must be divided to get a perfect square?
  26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 154 (b) 166 (c) 144
  28. 28.What is 79²? =
  29. 29.A square garden has an area of 2809 square m. How long is each side (in m)?
  30. 30.What is √5776? =
  31. 31.How many whole numbers lie between 25² and 26²?
  32. 32.A square garden has an area of 1600 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 784 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 117 (b) 110 (c) 100
  35. 35.A square garden has an area of 2116 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 576 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 225 square m. How long is each side (in m)?
  39. 39.What is 91²? =
  40. 40.What is 52²? =

Answer key

  1. 63
  2. 36
  3. 31
  4. 25
  5. 676
  6. 361
  7. 10
  8. 10
  9. 52
  10. 57
  11. 8649
  12. 60
  13. 10
  14. 31
  15. 51
  16. 76
  17. 196
  18. 16
  19. 676
  20. 1156
  21. 3249
  22. 85
  23. 5476
  24. 121
  25. 7
  26. 289
  27. 144
  28. 6241
  29. 53
  30. 76
  31. 50
  32. 40
  33. 28
  34. 100
  35. 46
  36. 64
  37. 24
  38. 15
  39. 8281
  40. 2704

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