← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 590 · 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 √484? =
  2. 2.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √8464? =
  4. 4.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  5. 5.What is the smallest whole number by which 448 must be divided to get a perfect square?
  6. 6.How many whole numbers lie between 14² and 15²?
  7. 7.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 122 (b) 121 (c) 127
  9. 9.Which of these is a perfect square? (a) 1480 (b) 1450 (c) 1444
  10. 10.How many whole numbers lie between 42² and 43²?
  11. 11.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is 84²? =
  14. 14.What is 66²? =
  15. 15.A square garden has an area of 64 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  17. 17.What is the smallest whole number by which 891 must be divided to get a perfect square?
  18. 18.How many whole numbers lie between 22² and 23²?
  19. 19.What is 32²? =
  20. 20.What is √7225? =
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  22. 22.Which of these is a perfect square? (a) 1432 (b) 1369 (c) 1442
  23. 23.How many whole numbers lie between 27² and 28²?
  24. 24.What is the smallest whole number by which 12 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 1129 (b) 1127 (c) 1089
  26. 26.How many whole numbers lie between 13² and 14²?
  27. 27.What is the smallest whole number by which 24 must be divided to get a perfect square?
  28. 28.What is 77²? =
  29. 29.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  30. 30.How many whole numbers lie between 36² and 37²?
  31. 31.What is 14²? =
  32. 32.Which of these is a perfect square? (a) 1600 (b) 1660 (c) 1612
  33. 33.What is 33²? =
  34. 34.How many whole numbers lie between 9² and 10²?
  35. 35.Which of these is a perfect square? (a) 390 (b) 361 (c) 366
  36. 36.What is 30²? =
  37. 37.What is 20²? =
  38. 38.What is √9409? =
  39. 39.What is 23²? =
  40. 40.A square garden has an area of 1936 square m. How long is each side (in m)?

Answer key

  1. 22
  2. 441
  3. 92
  4. 3
  5. 7
  6. 28
  7. 5
  8. 121
  9. 1444
  10. 84
  11. 11
  12. 49
  13. 7056
  14. 4356
  15. 8
  16. 15
  17. 11
  18. 44
  19. 1024
  20. 85
  21. 484
  22. 1369
  23. 54
  24. 3
  25. 1089
  26. 26
  27. 6
  28. 5929
  29. 11
  30. 72
  31. 196
  32. 1600
  33. 1089
  34. 18
  35. 361
  36. 900
  37. 400
  38. 97
  39. 529
  40. 44

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