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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 430 · 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 74²? =
  2. 2.A square garden has an area of 576 square m. How long is each side (in m)?
  3. 3.Which of these is a perfect square? (a) 260 (b) 264 (c) 256
  4. 4.What is 26²? =
  5. 5.Which of these is a perfect square? (a) 637 (b) 653 (c) 625
  6. 6.What is √2304? =
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  9. 9.What is 16²? =
  10. 10.A square garden has an area of 289 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  12. 12.What is 88²? =
  13. 13.What is the smallest whole number by which 96 must be divided to get a perfect square?
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 307 (b) 296 (c) 289
  16. 16.What is 34²? =
  17. 17.What is √1936? =
  18. 18.How many whole numbers lie between 46² and 47²?
  19. 19.How many whole numbers lie between 9² and 10²?
  20. 20.What is 87²? =
  21. 21.What is the smallest whole number by which 343 must be divided to get a perfect square?
  22. 22.What is 82²? =
  23. 23.A square garden has an area of 3364 square m. How long is each side (in m)?
  24. 24.What is 27²? =
  25. 25.Which of these is a perfect square? (a) 748 (b) 729 (c) 737
  26. 26.What is √841? =
  27. 27.How many whole numbers lie between 27² and 28²?
  28. 28.What is √6889? =
  29. 29.What is 36²? =
  30. 30.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √625? =
  33. 33.What is √2704? =
  34. 34.A square garden has an area of 3136 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  36. 36.A square garden has an area of 2500 square m. How long is each side (in m)?
  37. 37.What is 47²? =
  38. 38.A square garden has an area of 1089 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  40. 40.What is √2209? =

Answer key

  1. 5476
  2. 24
  3. 256
  4. 676
  5. 625
  6. 48
  7. 81
  8. 11
  9. 256
  10. 17
  11. 3
  12. 7744
  13. 6
  14. 47
  15. 289
  16. 1156
  17. 44
  18. 92
  19. 18
  20. 7569
  21. 7
  22. 6724
  23. 58
  24. 729
  25. 729
  26. 29
  27. 54
  28. 83
  29. 1296
  30. 6
  31. 576
  32. 25
  33. 52
  34. 56
  35. 14
  36. 50
  37. 2209
  38. 33
  39. 15
  40. 47

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