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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 396 · 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.Which of these is a perfect square? (a) 293 (b) 289 (c) 320
  2. 2.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 7² and 8²?
  4. 4.A square garden has an area of 2809 square m. How long is each side (in m)?
  5. 5.What is √1225? =
  6. 6.What is the smallest whole number by which 56 must be divided to get a perfect square?
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √1936? =
  9. 9.What is √1849? =
  10. 10.What is √144? =
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is 29²? =
  14. 14.What is √1681? =
  15. 15.What is √6889? =
  16. 16.A square garden has an area of 196 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  18. 18.What is √3844? =
  19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 400 (b) 418 (c) 401
  21. 21.What is the smallest whole number by which 350 must be divided to get a perfect square?
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √9801? =
  24. 24.What is 95²? =
  25. 25.How many whole numbers lie between 36² and 37²?
  26. 26.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  27. 27.What is 14²? =
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 961 square m. How long is each side (in m)?
  30. 30.What is √4489? =
  31. 31.A square garden has an area of 1089 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 158 (b) 161 (c) 144
  33. 33.How many whole numbers lie between 40² and 41²?
  34. 34.What is 82²? =
  35. 35.What is 97²? =
  36. 36.What is the smallest whole number by which 245 must be divided to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 274 (b) 288 (c) 256
  38. 38.What is √4225? =
  39. 39.What is the smallest whole number by which 224 must be divided to get a perfect square?
  40. 40.How many whole numbers lie between 43² and 44²?

Answer key

  1. 289
  2. 3
  3. 14
  4. 53
  5. 35
  6. 14
  7. 729
  8. 44
  9. 43
  10. 12
  11. 900
  12. 289
  13. 841
  14. 41
  15. 83
  16. 14
  17. 13
  18. 62
  19. 144
  20. 400
  21. 14
  22. 100
  23. 99
  24. 9025
  25. 72
  26. 15
  27. 196
  28. 441
  29. 31
  30. 67
  31. 33
  32. 144
  33. 80
  34. 6724
  35. 9409
  36. 5
  37. 256
  38. 65
  39. 14
  40. 86

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