← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 197 · 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 √1024? =
  2. 2.What is 96²? =
  3. 3.Which of these is a perfect square? (a) 259 (b) 262 (c) 256
  4. 4.What is the smallest whole number by which 162 must be divided to get a perfect square?
  5. 5.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 28² and 29²?
  7. 7.What is the smallest whole number by which 540 must be divided to get a perfect square?
  8. 8.How many whole numbers lie between 48² and 49²?
  9. 9.What is 25²? =
  10. 10.How many whole numbers lie between 15² and 16²?
  11. 11.A square garden has an area of 100 square m. How long is each side (in m)?
  12. 12.What is √9801? =
  13. 13.What is √6400? =
  14. 14.Which of these is a perfect square? (a) 999 (b) 1010 (c) 961
  15. 15.What is the smallest whole number by which 896 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 35² and 36²?
  17. 17.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 64 square m. How long is each side (in m)?
  19. 19.What is 99²? =
  20. 20.Which of these is a perfect square? (a) 361 (b) 381 (c) 391
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √196? =
  23. 23.Which of these is a perfect square? (a) 834 (b) 795 (c) 784
  24. 24.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 2401 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 1037 (b) 1045 (c) 1024
  28. 28.What is 94²? =
  29. 29.What is 19²? =
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 122 (b) 121 (c) 131
  32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is √8100? =
  34. 34.What is 23²? =
  35. 35.What is the smallest whole number by which 448 must be divided to get a perfect square?
  36. 36.A square garden has an area of 729 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 10² and 11²?
  38. 38.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  39. 39.What is √1849? =
  40. 40.Which of these is a perfect square? (a) 876 (b) 857 (c) 841

Answer key

  1. 32
  2. 9216
  3. 256
  4. 2
  5. 400
  6. 56
  7. 15
  8. 96
  9. 625
  10. 30
  11. 10
  12. 99
  13. 80
  14. 961
  15. 14
  16. 70
  17. 11
  18. 8
  19. 9801
  20. 361
  21. 576
  22. 14
  23. 784
  24. 10
  25. 36
  26. 49
  27. 1024
  28. 8836
  29. 361
  30. 81
  31. 121
  32. 784
  33. 90
  34. 529
  35. 7
  36. 27
  37. 20
  38. 14
  39. 43
  40. 841

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