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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 607 · 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 32²? =
  2. 2.A square garden has an area of 36 square m. How long is each side (in m)?
  3. 3.What is 44²? =
  4. 4.What is 12²? =
  5. 5.Which of these is a perfect square? (a) 651 (b) 625 (c) 669
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 836 (b) 784 (c) 788
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √8836? =
  10. 10.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 2601 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  13. 13.Which of these is a perfect square? (a) 112 (b) 100 (c) 118
  14. 14.Which of these is a perfect square? (a) 1369 (b) 1371 (c) 1383
  15. 15.What is √2916? =
  16. 16.What is √9801? =
  17. 17.Which of these is a perfect square? (a) 1365 (b) 1319 (c) 1296
  18. 18.What is √576? =
  19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 11²? =
  21. 21.A square garden has an area of 1024 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 108 must be divided to get a perfect square?
  24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 60²? =
  26. 26.What is the smallest whole number by which 45 must be divided to get a perfect square?
  27. 27.How many whole numbers lie between 16² and 17²?
  28. 28.What is the smallest whole number by which 486 must be divided to get a perfect square?
  29. 29.A square garden has an area of 2116 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 225 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  33. 33.What is √3969? =
  34. 34.How many whole numbers lie between 35² and 36²?
  35. 35.Which of these is a perfect square? (a) 156 (b) 144 (c) 148
  36. 36.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 2704 square m. How long is each side (in m)?
  38. 38.What is √3721? =
  39. 39.What is √1296? =
  40. 40.What is 58²? =

Answer key

  1. 1024
  2. 6
  3. 1936
  4. 144
  5. 625
  6. 289
  7. 784
  8. 100
  9. 94
  10. 3
  11. 51
  12. 36
  13. 100
  14. 1369
  15. 54
  16. 99
  17. 1296
  18. 24
  19. 784
  20. 121
  21. 32
  22. 324
  23. 3
  24. 169
  25. 3600
  26. 5
  27. 32
  28. 6
  29. 46
  30. 15
  31. 7
  32. 15
  33. 63
  34. 70
  35. 144
  36. 2
  37. 52
  38. 61
  39. 36
  40. 3364

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