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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 303 · 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.A square garden has an area of 2209 square m. How long is each side (in m)?
  2. 2.What is 94²? =
  3. 3.A square garden has an area of 2601 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 3025 square m. How long is each side (in m)?
  5. 5.How many whole numbers lie between 38² and 39²?
  6. 6.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  7. 7.What is 28²? =
  8. 8.Which of these is a perfect square? (a) 396 (b) 361 (c) 391
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  11. 11.What is the smallest whole number by which 375 must be divided to get a perfect square?
  12. 12.What is 70²? =
  13. 13.What is 17²? =
  14. 14.What is 38²? =
  15. 15.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  16. 16.What is the smallest whole number by which 224 must be divided to get a perfect square?
  17. 17.What is 51²? =
  18. 18.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 529 square m. How long is each side (in m)?
  20. 20.What is √6561? =
  21. 21.How many whole numbers lie between 6² and 7²?
  22. 22.What is √4900? =
  23. 23.A square garden has an area of 361 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  25. 25.How many whole numbers lie between 36² and 37²?
  26. 26.A square garden has an area of 484 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 213 (b) 196 (c) 209
  28. 28.What is 88²? =
  29. 29.How many whole numbers lie between 10² and 11²?
  30. 30.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  31. 31.What is 61²? =
  32. 32.Which of these is a perfect square? (a) 1655 (b) 1600 (c) 1671
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is √2916? =
  35. 35.What is √256? =
  36. 36.What is √4489? =
  37. 37.How many whole numbers lie between 9² and 10²?
  38. 38.Which of these is a perfect square? (a) 279 (b) 256 (c) 275
  39. 39.What is √8836? =
  40. 40.How many whole numbers lie between 32² and 33²?

Answer key

  1. 47
  2. 8836
  3. 51
  4. 55
  5. 76
  6. 5
  7. 784
  8. 361
  9. 400
  10. 11
  11. 15
  12. 4900
  13. 289
  14. 1444
  15. 6
  16. 14
  17. 2601
  18. 64
  19. 23
  20. 81
  21. 12
  22. 70
  23. 19
  24. 10
  25. 72
  26. 22
  27. 196
  28. 7744
  29. 20
  30. 15
  31. 3721
  32. 1600
  33. 256
  34. 54
  35. 16
  36. 67
  37. 18
  38. 256
  39. 94
  40. 64

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