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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 283 · 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 √7744? =
  2. 2.What is 33²? =
  3. 3.What is √324? =
  4. 4.Which of these is a perfect square? (a) 192 (b) 169 (c) 188
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 5² and 6²?
  7. 7.What is √7225? =
  8. 8.What is √7569? =
  9. 9.What is the smallest whole number by which 704 must be divided to get a perfect square?
  10. 10.How many whole numbers lie between 26² and 27²?
  11. 11.A square garden has an area of 1296 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √1764? =
  14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √729? =
  18. 18.What is 79²? =
  19. 19.What is 99²? =
  20. 20.What is 25²? =
  21. 21.Which of these is a perfect square? (a) 654 (b) 648 (c) 625
  22. 22.What is 30²? =
  23. 23.How many whole numbers lie between 16² and 17²?
  24. 24.What is the smallest whole number by which 176 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 1600 (b) 1670 (c) 1607
  26. 26.What is the smallest whole number by which 63 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 121 (b) 143 (c) 140
  28. 28.Which of these is a perfect square? (a) 144 (b) 146 (c) 148
  29. 29.What is 13²? =
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 16²? =
  32. 32.A square garden has an area of 3364 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 37² and 38²?
  35. 35.What is 29²? =
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √4225? =
  38. 38.What is √6889? =
  39. 39.What is the smallest whole number by which 147 must be divided to get a perfect square?
  40. 40.A square garden has an area of 3600 square m. How long is each side (in m)?

Answer key

  1. 88
  2. 1089
  3. 18
  4. 169
  5. 196
  6. 10
  7. 85
  8. 87
  9. 11
  10. 52
  11. 36
  12. 729
  13. 42
  14. 49
  15. 2
  16. 121
  17. 27
  18. 6241
  19. 9801
  20. 625
  21. 625
  22. 900
  23. 32
  24. 11
  25. 1600
  26. 7
  27. 121
  28. 144
  29. 169
  30. 25
  31. 256
  32. 58
  33. 400
  34. 74
  35. 841
  36. 169
  37. 65
  38. 83
  39. 3
  40. 60

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