← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 725 · 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 84²? =
  2. 2.What is √6724? =
  3. 3.Which of these is a perfect square? (a) 761 (b) 729 (c) 754
  4. 4.A square garden has an area of 25 square m. How long is each side (in m)?
  5. 5.What is 70²? =
  6. 6.What is 74²? =
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 64²? =
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 2401 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 30² and 31²?
  13. 13.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 18² and 19²?
  15. 15.Which of these is a perfect square? (a) 1049 (b) 1024 (c) 1067
  16. 16.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 1401 (b) 1369 (c) 1414
  18. 18.A square garden has an area of 2025 square m. How long is each side (in m)?
  19. 19.A square garden has an area of 1369 square m. How long is each side (in m)?
  20. 20.What is √1089? =
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 49² and 50²?
  24. 24.How many whole numbers lie between 17² and 18²?
  25. 25.What is 40²? =
  26. 26.What is 24²? =
  27. 27.Which of these is a perfect square? (a) 1161 (b) 1218 (c) 1156
  28. 28.How many whole numbers lie between 50² and 51²?
  29. 29.What is √484? =
  30. 30.How many whole numbers lie between 47² and 48²?
  31. 31.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 42² and 43²?
  34. 34.What is 20²? =
  35. 35.What is √9216? =
  36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √1600? =
  38. 38.What is √4900? =
  39. 39.A square garden has an area of 625 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 495 (b) 485 (c) 484

Answer key

  1. 7056
  2. 82
  3. 729
  4. 5
  5. 4900
  6. 5476
  7. 144
  8. 4096
  9. 784
  10. 100
  11. 49
  12. 60
  13. 6
  14. 36
  15. 1024
  16. 625
  17. 1369
  18. 45
  19. 37
  20. 33
  21. 289
  22. 81
  23. 98
  24. 34
  25. 1600
  26. 576
  27. 1156
  28. 100
  29. 22
  30. 94
  31. 900
  32. 676
  33. 84
  34. 400
  35. 96
  36. 729
  37. 40
  38. 70
  39. 25
  40. 484

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