← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 349 · 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 12² and 13²?
  2. 2.What is √2401? =
  3. 3.How many whole numbers lie between 15² and 16²?
  4. 4.Which of these is a perfect square? (a) 1368 (b) 1323 (c) 1296
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  6. 6.Which of these is a perfect square? (a) 168 (b) 144 (c) 147
  7. 7.What is the smallest whole number by which 150 must be divided to get a perfect square?
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 441 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 62²? =
  13. 13.Which of these is a perfect square? (a) 324 (b) 335 (c) 337
  14. 14.What is 64²? =
  15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 94²? =
  17. 17.Which of these is a perfect square? (a) 274 (b) 256 (c) 280
  18. 18.How many whole numbers lie between 6² and 7²?
  19. 19.What is the smallest whole number by which 637 must be divided to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 1520 (b) 1508 (c) 1444
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  23. 23.Which of these is a perfect square? (a) 953 (b) 938 (c) 900
  24. 24.Which of these is a perfect square? (a) 961 (b) 969 (c) 987
  25. 25.A square garden has an area of 484 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 405 must be divided to get a perfect square?
  27. 27.What is 84²? =
  28. 28.How many whole numbers lie between 28² and 29²?
  29. 29.A square garden has an area of 676 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 72 must be divided to get a perfect square?
  31. 31.What is the smallest whole number by which 135 must be divided to get a perfect square?
  32. 32.What is √1089? =
  33. 33.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  34. 34.How many whole numbers lie between 27² and 28²?
  35. 35.What is 25²? =
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  37. 37.Which of these is a perfect square? (a) 1088 (b) 1031 (c) 1024
  38. 38.How many whole numbers lie between 17² and 18²?
  39. 39.How many whole numbers lie between 14² and 15²?
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 24
  2. 49
  3. 30
  4. 1296
  5. 49
  6. 144
  7. 6
  8. 256
  9. 121
  10. 21
  11. 900
  12. 3844
  13. 324
  14. 4096
  15. 676
  16. 8836
  17. 256
  18. 12
  19. 13
  20. 1444
  21. 36
  22. 529
  23. 900
  24. 961
  25. 22
  26. 5
  27. 7056
  28. 56
  29. 26
  30. 2
  31. 15
  32. 33
  33. 13
  34. 54
  35. 625
  36. 100
  37. 1024
  38. 34
  39. 28
  40. 441

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