← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 363 · 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 √6400? =
  2. 2.What is the smallest whole number by which 125 must be divided to get a perfect square?
  3. 3.What is the smallest whole number by which 27 must be divided to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 145 (b) 144 (c) 155
  5. 5.How many whole numbers lie between 6² and 7²?
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √144? =
  9. 9.What is 25²? =
  10. 10.What is 64²? =
  11. 11.What is 85²? =
  12. 12.What is 80²? =
  13. 13.Which of these is a perfect square? (a) 1330 (b) 1319 (c) 1296
  14. 14.A square garden has an area of 2304 square m. How long is each side (in m)?
  15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 13² and 14²?
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √5041? =
  19. 19.What is 32²? =
  20. 20.How many whole numbers lie between 7² and 8²?
  21. 21.What is 15²? =
  22. 22.Which of these is a perfect square? (a) 1041 (b) 1024 (c) 1046
  23. 23.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 3600 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 42² and 43²?
  27. 27.How many whole numbers lie between 11² and 12²?
  28. 28.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 216 (b) 196 (c) 218
  30. 30.What is 47²? =
  31. 31.What is the smallest whole number by which 28 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 790 (b) 801 (c) 784
  33. 33.What is 75²? =
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √7396? =
  36. 36.Which of these is a perfect square? (a) 616 (b) 596 (c) 576
  37. 37.How many whole numbers lie between 31² and 32²?
  38. 38.What is 54²? =
  39. 39.Which of these is a perfect square? (a) 1225 (b) 1279 (c) 1277
  40. 40.What is √784? =

Answer key

  1. 80
  2. 5
  3. 3
  4. 144
  5. 12
  6. 49
  7. 64
  8. 12
  9. 625
  10. 4096
  11. 7225
  12. 6400
  13. 1296
  14. 48
  15. 729
  16. 26
  17. 289
  18. 71
  19. 1024
  20. 14
  21. 225
  22. 1024
  23. 10
  24. 81
  25. 60
  26. 84
  27. 22
  28. 10
  29. 196
  30. 2209
  31. 7
  32. 784
  33. 5625
  34. 196
  35. 86
  36. 576
  37. 62
  38. 2916
  39. 1225
  40. 28

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