← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 458 · 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 21 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 361 (b) 364 (c) 392
  3. 3.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  4. 4.What is 16²? =
  5. 5.How many whole numbers lie between 27² and 28²?
  6. 6.How many whole numbers lie between 24² and 25²?
  7. 7.Which of these is a perfect square? (a) 1000 (b) 961 (c) 982
  8. 8.A square garden has an area of 400 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 1531 (b) 1573 (c) 1521
  10. 10.A square garden has an area of 1936 square m. How long is each side (in m)?
  11. 11.What is 98²? =
  12. 12.Which of these is a perfect square? (a) 177 (b) 195 (c) 169
  13. 13.Which of these is a perfect square? (a) 158 (b) 147 (c) 144
  14. 14.What is √1089? =
  15. 15.Which of these is a perfect square? (a) 1156 (b) 1183 (c) 1164
  16. 16.Which of these is a perfect square? (a) 123 (b) 138 (c) 121
  17. 17.How many whole numbers lie between 11² and 12²?
  18. 18.How many whole numbers lie between 32² and 33²?
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is 47²? =
  21. 21.A square garden has an area of 1089 square m. How long is each side (in m)?
  22. 22.What is 86²? =
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √324? =
  25. 25.A square garden has an area of 2401 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.How many whole numbers lie between 19² and 20²?
  29. 29.Which of these is a perfect square? (a) 1395 (b) 1385 (c) 1369
  30. 30.A square garden has an area of 121 square m. How long is each side (in m)?
  31. 31.What is 13²? =
  32. 32.What is √4624? =
  33. 33.Which of these is a perfect square? (a) 285 (b) 256 (c) 280
  34. 34.What is √576? =
  35. 35.How many whole numbers lie between 10² and 11²?
  36. 36.How many whole numbers lie between 35² and 36²?
  37. 37.What is √8836? =
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √4489? =
  40. 40.Which of these is a perfect square? (a) 1237 (b) 1225 (c) 1259

Answer key

  1. 441
  2. 361
  3. 13
  4. 256
  5. 54
  6. 48
  7. 961
  8. 20
  9. 1521
  10. 44
  11. 9604
  12. 169
  13. 144
  14. 33
  15. 1156
  16. 121
  17. 22
  18. 64
  19. 121
  20. 2209
  21. 33
  22. 7396
  23. 900
  24. 18
  25. 49
  26. 256
  27. 49
  28. 38
  29. 1369
  30. 11
  31. 169
  32. 68
  33. 256
  34. 24
  35. 20
  36. 70
  37. 94
  38. 144
  39. 67
  40. 1225

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