← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 639 · 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 smallest whole number by which 405 must be divided to get a perfect square?
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 729 square m. How long is each side (in m)?
  5. 5.What is 74²? =
  6. 6.What is 57²? =
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 125 (b) 121 (c) 142
  9. 9.How many whole numbers lie between 41² and 42²?
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 205 (b) 196 (c) 199
  12. 12.What is √324? =
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 118 (b) 119 (c) 100
  15. 15.What is √8649? =
  16. 16.Which of these is a perfect square? (a) 986 (b) 1001 (c) 961
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 384 must be divided to get a perfect square?
  19. 19.What is √1764? =
  20. 20.A square garden has an area of 81 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 891 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 709 (b) 676 (c) 721
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 25² and 26²?
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 98²? =
  27. 27.What is the smallest whole number by which 50 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 33² and 34²?
  29. 29.A square garden has an area of 1764 square m. How long is each side (in m)?
  30. 30.What is 31²? =
  31. 31.What is the smallest whole number by which 112 must be divided to get a perfect square?
  32. 32.A square garden has an area of 3364 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 27² and 28²?
  34. 34.What is 43²? =
  35. 35.What is √441? =
  36. 36.How many whole numbers lie between 43² and 44²?
  37. 37.A square garden has an area of 484 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  39. 39.What is √5041? =
  40. 40.What is √5476? =

Answer key

  1. 5
  2. 36
  3. 441
  4. 27
  5. 5476
  6. 3249
  7. 289
  8. 121
  9. 82
  10. 225
  11. 196
  12. 18
  13. 144
  14. 100
  15. 93
  16. 961
  17. 400
  18. 6
  19. 42
  20. 9
  21. 11
  22. 676
  23. 25
  24. 50
  25. 729
  26. 9604
  27. 2
  28. 66
  29. 42
  30. 961
  31. 7
  32. 58
  33. 54
  34. 1849
  35. 21
  36. 86
  37. 22
  38. 2
  39. 71
  40. 74

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