← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 364 · 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.How many whole numbers lie between 17² and 18²?
  2. 2.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 3025 square m. How long is each side (in m)?
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 196 square m. How long is each side (in m)?
  6. 6.What is √1369? =
  7. 7.How many whole numbers lie between 44² and 45²?
  8. 8.What is √8464? =
  9. 9.What is √1089? =
  10. 10.What is 52²? =
  11. 11.A square garden has an area of 400 square m. How long is each side (in m)?
  12. 12.What is 50²? =
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √7921? =
  15. 15.What is 12²? =
  16. 16.How many whole numbers lie between 16² and 17²?
  17. 17.Which of these is a perfect square? (a) 1217 (b) 1156 (c) 1188
  18. 18.What is 81²? =
  19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  22. 22.A square garden has an area of 1444 square m. How long is each side (in m)?
  23. 23.What is 36²? =
  24. 24.What is √3364? =
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √7569? =
  27. 27.What is 53²? =
  28. 28.How many whole numbers lie between 5² and 6²?
  29. 29.What is √5929? =
  30. 30.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  31. 31.What is 21²? =
  32. 32.A square garden has an area of 2704 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  34. 34.A square garden has an area of 256 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 36 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 669 (b) 637 (c) 625
  37. 37.How many whole numbers lie between 49² and 50²?
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 26²? =
  40. 40.What is the smallest whole number by which 245 must be multiplied to get a perfect square?

Answer key

  1. 34
  2. 11
  3. 55
  4. 36
  5. 14
  6. 37
  7. 88
  8. 92
  9. 33
  10. 2704
  11. 20
  12. 2500
  13. 900
  14. 89
  15. 144
  16. 32
  17. 1156
  18. 6561
  19. 196
  20. 6
  21. 7
  22. 38
  23. 1296
  24. 58
  25. 25
  26. 87
  27. 2809
  28. 10
  29. 77
  30. 6
  31. 441
  32. 52
  33. 5
  34. 16
  35. 6
  36. 625
  37. 98
  38. 289
  39. 676
  40. 5

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