← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 195 · 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 √1369? =
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 133 (b) 142 (c) 121
  4. 4.A square garden has an area of 1444 square m. How long is each side (in m)?
  5. 5.What is 70²? =
  6. 6.Which of these is a perfect square? (a) 324 (b) 337 (c) 332
  7. 7.Which of these is a perfect square? (a) 729 (b) 740 (c) 748
  8. 8.How many whole numbers lie between 9² and 10²?
  9. 9.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  10. 10.A square garden has an area of 729 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is √784? =
  13. 13.What is √4900? =
  14. 14.Which of these is a perfect square? (a) 296 (b) 290 (c) 289
  15. 15.What is 69²? =
  16. 16.A square garden has an area of 2704 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 11² and 12²?
  18. 18.What is 72²? =
  19. 19.What is √2209? =
  20. 20.What is 77²? =
  21. 21.A square garden has an area of 484 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 1849 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  24. 24.Which of these is a perfect square? (a) 1311 (b) 1315 (c) 1296
  25. 25.What is 12²? =
  26. 26.What is 58²? =
  27. 27.How many whole numbers lie between 13² and 14²?
  28. 28.A square garden has an area of 961 square m. How long is each side (in m)?
  29. 29.What is √6084? =
  30. 30.What is the smallest whole number by which 44 must be divided to get a perfect square?
  31. 31.How many whole numbers lie between 46² and 47²?
  32. 32.What is √8100? =
  33. 33.What is 29²? =
  34. 34.A square garden has an area of 625 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  36. 36.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  37. 37.How many whole numbers lie between 40² and 41²?
  38. 38.How many whole numbers lie between 31² and 32²?
  39. 39.How many whole numbers lie between 30² and 31²?
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 37
  2. 81
  3. 121
  4. 38
  5. 4900
  6. 324
  7. 729
  8. 18
  9. 15
  10. 27
  11. 36
  12. 28
  13. 70
  14. 289
  15. 4761
  16. 52
  17. 22
  18. 5184
  19. 47
  20. 5929
  21. 22
  22. 43
  23. 15
  24. 1296
  25. 144
  26. 3364
  27. 26
  28. 31
  29. 78
  30. 11
  31. 92
  32. 90
  33. 841
  34. 25
  35. 14
  36. 3
  37. 80
  38. 62
  39. 60
  40. 64

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