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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 233 · 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.How many whole numbers lie between 5² and 6²?
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  4. 4.What is √5329? =
  5. 5.What is 18²? =
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √3136? =
  9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 2601 square m. How long is each side (in m)?
  11. 11.What is 56²? =
  12. 12.What is √6084? =
  13. 13.How many whole numbers lie between 46² and 47²?
  14. 14.A square garden has an area of 1156 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 1681 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 676 (b) 719 (c) 708
  17. 17.How many whole numbers lie between 17² and 18²?
  18. 18.What is the smallest whole number by which 126 must be divided to get a perfect square?
  19. 19.Which of these is a perfect square? (a) 347 (b) 345 (c) 324
  20. 20.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 494 (b) 492 (c) 484
  22. 22.What is the smallest whole number by which 75 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 7² and 8²?
  24. 24.What is √1089? =
  25. 25.What is 22²? =
  26. 26.A square garden has an area of 25 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 224 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 11² and 12²?
  29. 29.What is 12²? =
  30. 30.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √4489? =
  32. 32.What is √1024? =
  33. 33.What is 55²? =
  34. 34.What is 16²? =
  35. 35.What is 98²? =
  36. 36.A square garden has an area of 100 square m. How long is each side (in m)?
  37. 37.What is 96²? =
  38. 38.A square garden has an area of 81 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 173 (b) 195 (c) 169
  40. 40.Which of these is a perfect square? (a) 304 (b) 314 (c) 289

Answer key

  1. 10
  2. 121
  3. 10
  4. 73
  5. 324
  6. 100
  7. 36
  8. 56
  9. 12
  10. 51
  11. 3136
  12. 78
  13. 92
  14. 34
  15. 41
  16. 676
  17. 34
  18. 14
  19. 324
  20. 13
  21. 484
  22. 3
  23. 14
  24. 33
  25. 484
  26. 5
  27. 14
  28. 22
  29. 144
  30. 784
  31. 67
  32. 32
  33. 3025
  34. 256
  35. 9604
  36. 10
  37. 9216
  38. 9
  39. 169
  40. 289

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