← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 71 · 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 √5329? =
  2. 2.Which of these is a perfect square? (a) 676 (b) 699 (c) 693
  3. 3.What is the smallest whole number by which 325 must be divided to get a perfect square?
  4. 4.What is the smallest whole number by which 240 must be divided to get a perfect square?
  5. 5.A square garden has an area of 2304 square m. How long is each side (in m)?
  6. 6.How many whole numbers lie between 9² and 10²?
  7. 7.Which of these is a perfect square? (a) 196 (b) 211 (c) 201
  8. 8.A square garden has an area of 2704 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 483 (b) 444 (c) 441
  11. 11.What is the smallest whole number by which 28 must be divided to get a perfect square?
  12. 12.How many whole numbers lie between 12² and 13²?
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √4900? =
  15. 15.What is the smallest whole number by which 24 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 320 must be divided to get a perfect square?
  17. 17.What is √8100? =
  18. 18.Which of these is a perfect square? (a) 860 (b) 881 (c) 841
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 34² and 35²?
  21. 21.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 2401 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 1296 square m. How long is each side (in m)?
  24. 24.What is √529? =
  25. 25.What is 50²? =
  26. 26.How many whole numbers lie between 26² and 27²?
  27. 27.A square garden has an area of 529 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 2500 square m. How long is each side (in m)?
  29. 29.What is √5776? =
  30. 30.What is √6724? =
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 45² and 46²?
  33. 33.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  34. 34.What is 78²? =
  35. 35.What is √1600? =
  36. 36.What is √5041? =
  37. 37.What is 81²? =
  38. 38.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  39. 39.What is 98²? =
  40. 40.A square garden has an area of 2209 square m. How long is each side (in m)?

Answer key

  1. 73
  2. 676
  3. 13
  4. 15
  5. 48
  6. 18
  7. 196
  8. 52
  9. 576
  10. 441
  11. 7
  12. 24
  13. 841
  14. 70
  15. 6
  16. 5
  17. 90
  18. 841
  19. 121
  20. 68
  21. 625
  22. 49
  23. 36
  24. 23
  25. 2500
  26. 52
  27. 23
  28. 50
  29. 76
  30. 82
  31. 64
  32. 90
  33. 2
  34. 6084
  35. 40
  36. 71
  37. 6561
  38. 7
  39. 9604
  40. 47

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