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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 572 · 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 78²? =
  2. 2.A square garden has an area of 1936 square m. How long is each side (in m)?
  3. 3.What is √7744? =
  4. 4.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  5. 5.What is √729? =
  6. 6.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  7. 7.How many whole numbers lie between 46² and 47²?
  8. 8.What is 27²? =
  9. 9.What is √5184? =
  10. 10.A square garden has an area of 900 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  12. 12.What is √5625? =
  13. 13.What is the smallest whole number by which 360 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 1240 (b) 1225 (c) 1234
  15. 15.How many whole numbers lie between 11² and 12²?
  16. 16.Which of these is a perfect square? (a) 900 (b) 941 (c) 908
  17. 17.What is √7396? =
  18. 18.How many whole numbers lie between 5² and 6²?
  19. 19.What is 13²? =
  20. 20.What is the smallest whole number by which 384 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 100 (b) 112 (c) 104
  22. 22.What is √4225? =
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 17² and 18²?
  25. 25.What is √3844? =
  26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is 30²? =
  28. 28.How many whole numbers lie between 33² and 34²?
  29. 29.How many whole numbers lie between 24² and 25²?
  30. 30.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 26²? =
  32. 32.What is 32²? =
  33. 33.A square garden has an area of 3136 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 8² and 9²?
  35. 35.A square garden has an area of 1156 square m. How long is each side (in m)?
  36. 36.What is √4096? =
  37. 37.A square garden has an area of 1681 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.A square garden has an area of 36 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 224 must be multiplied to get a perfect square?

Answer key

  1. 6084
  2. 44
  3. 88
  4. 3
  5. 27
  6. 7
  7. 92
  8. 729
  9. 72
  10. 30
  11. 11
  12. 75
  13. 10
  14. 1225
  15. 22
  16. 900
  17. 86
  18. 10
  19. 169
  20. 6
  21. 100
  22. 65
  23. 576
  24. 34
  25. 62
  26. 49
  27. 900
  28. 66
  29. 48
  30. 256
  31. 676
  32. 1024
  33. 56
  34. 16
  35. 34
  36. 64
  37. 41
  38. 60
  39. 6
  40. 14

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