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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 647 · 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 the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √2500? =
  3. 3.What is 27²? =
  4. 4.What is 46²? =
  5. 5.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √3481? =
  7. 7.What is 13²? =
  8. 8.What is 35²? =
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 68²? =
  11. 11.What is the smallest whole number by which 896 must be divided to get a perfect square?
  12. 12.What is the smallest whole number by which 8 must be divided to get a perfect square?
  13. 13.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  14. 14.What is √8649? =
  15. 15.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  16. 16.How many whole numbers lie between 46² and 47²?
  17. 17.What is the smallest whole number by which 99 must be divided to get a perfect square?
  18. 18.A square garden has an area of 1089 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 1568 (b) 1521 (c) 1596
  21. 21.What is the smallest whole number by which 960 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 441 (b) 443 (c) 447
  23. 23.How many whole numbers lie between 36² and 37²?
  24. 24.What is √676? =
  25. 25.Which of these is a perfect square? (a) 1063 (b) 1039 (c) 1024
  26. 26.A square garden has an area of 3136 square m. How long is each side (in m)?
  27. 27.What is √4761? =
  28. 28.What is √1764? =
  29. 29.What is √5625? =
  30. 30.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 13² and 14²?
  32. 32.A square garden has an area of 225 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 8² and 9²?
  34. 34.A square garden has an area of 441 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 10² and 11²?
  36. 36.A square garden has an area of 1849 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 3364 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 576 (b) 608 (c) 612
  39. 39.A square garden has an area of 1444 square m. How long is each side (in m)?
  40. 40.What is 67²? =

Answer key

  1. 81
  2. 50
  3. 729
  4. 2116
  5. 729
  6. 59
  7. 169
  8. 1225
  9. 256
  10. 4624
  11. 14
  12. 2
  13. 13
  14. 93
  15. 13
  16. 92
  17. 11
  18. 33
  19. 15
  20. 1521
  21. 15
  22. 441
  23. 72
  24. 26
  25. 1024
  26. 56
  27. 69
  28. 42
  29. 75
  30. 3
  31. 26
  32. 15
  33. 16
  34. 21
  35. 20
  36. 43
  37. 58
  38. 576
  39. 38
  40. 4489

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