← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 344 · 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 the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 13² and 14²?
  3. 3.What is 11²? =
  4. 4.What is 32²? =
  5. 5.What is the smallest whole number by which 40 must be divided to get a perfect square?
  6. 6.What is the smallest whole number by which 32 must be divided to get a perfect square?
  7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  10. 10.What is 83²? =
  11. 11.What is 74²? =
  12. 12.What is √2209? =
  13. 13.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  14. 14.What is 54²? =
  15. 15.A square garden has an area of 676 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  17. 17.What is 48²? =
  18. 18.What is the smallest whole number by which 396 must be divided to get a perfect square?
  19. 19.A square garden has an area of 3600 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 27² and 28²?
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 243 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 48² and 49²?
  24. 24.What is √3249? =
  25. 25.What is the smallest whole number by which 128 must be divided to get a perfect square?
  26. 26.What is 68²? =
  27. 27.Which of these is a perfect square? (a) 854 (b) 841 (c) 869
  28. 28.What is 66²? =
  29. 29.How many whole numbers lie between 6² and 7²?
  30. 30.What is 88²? =
  31. 31.What is the smallest whole number by which 735 must be divided to get a perfect square?
  32. 32.What is 51²? =
  33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 15² and 16²?
  35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 3136 square m. How long is each side (in m)?
  38. 38.What is √289? =
  39. 39.A square garden has an area of 2209 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 905 (b) 957 (c) 900

Answer key

  1. 900
  2. 26
  3. 121
  4. 1024
  5. 10
  6. 2
  7. 121
  8. 441
  9. 15
  10. 6889
  11. 5476
  12. 47
  13. 7
  14. 2916
  15. 26
  16. 6
  17. 2304
  18. 11
  19. 60
  20. 54
  21. 676
  22. 3
  23. 96
  24. 57
  25. 2
  26. 4624
  27. 841
  28. 4356
  29. 12
  30. 7744
  31. 15
  32. 2601
  33. 784
  34. 30
  35. 81
  36. 625
  37. 56
  38. 17
  39. 47
  40. 900

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets