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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 420 · 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.A square garden has an area of 2916 square m. How long is each side (in m)?
  2. 2.What is 36²? =
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 3364 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 60 must be divided to get a perfect square?
  6. 6.How many whole numbers lie between 45² and 46²?
  7. 7.How many whole numbers lie between 44² and 45²?
  8. 8.What is √1936? =
  9. 9.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 80 must be divided to get a perfect square?
  12. 12.What is √4225? =
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 29²? =
  15. 15.What is the smallest whole number by which 343 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 30² and 31²?
  17. 17.What is √3600? =
  18. 18.Which of these is a perfect square? (a) 411 (b) 400 (c) 424
  19. 19.A square garden has an area of 36 square m. How long is each side (in m)?
  20. 20.What is 61²? =
  21. 21.A square garden has an area of 121 square m. How long is each side (in m)?
  22. 22.What is √3481? =
  23. 23.What is 15²? =
  24. 24.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  25. 25.What is √784? =
  26. 26.Which of these is a perfect square? (a) 195 (b) 187 (c) 169
  27. 27.A square garden has an area of 1936 square m. How long is each side (in m)?
  28. 28.What is √2209? =
  29. 29.Which of these is a perfect square? (a) 878 (b) 841 (c) 869
  30. 30.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  31. 31.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  33. 33.What is √1156? =
  34. 34.A square garden has an area of 3136 square m. How long is each side (in m)?
  35. 35.What is 88²? =
  36. 36.What is 34²? =
  37. 37.A square garden has an area of 64 square m. How long is each side (in m)?
  38. 38.What is √1521? =
  39. 39.What is √2304? =
  40. 40.What is √9025? =

Answer key

  1. 54
  2. 1296
  3. 25
  4. 58
  5. 15
  6. 90
  7. 88
  8. 44
  9. 2
  10. 121
  11. 5
  12. 65
  13. 64
  14. 841
  15. 7
  16. 60
  17. 60
  18. 400
  19. 6
  20. 3721
  21. 11
  22. 59
  23. 225
  24. 11
  25. 28
  26. 169
  27. 44
  28. 47
  29. 841
  30. 5
  31. 14
  32. 2
  33. 34
  34. 56
  35. 7744
  36. 1156
  37. 8
  38. 39
  39. 48
  40. 95

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