← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 133 · 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 36²? =
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 21² and 22²?
  4. 4.What is √144? =
  5. 5.A square garden has an area of 1296 square m. How long is each side (in m)?
  6. 6.What is 20²? =
  7. 7.What is √6889? =
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 332 (b) 360 (c) 324
  10. 10.What is √2704? =
  11. 11.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 169 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 289 (b) 293 (c) 291
  14. 14.What is 40²? =
  15. 15.What is √1089? =
  16. 16.How many whole numbers lie between 14² and 15²?
  17. 17.What is 16²? =
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1108 (b) 1137 (c) 1089
  20. 20.Which of these is a perfect square? (a) 794 (b) 812 (c) 784
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 37² and 38²?
  23. 23.What is the smallest whole number by which 704 must be divided to get a perfect square?
  24. 24.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  27. 27.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  28. 28.A square garden has an area of 441 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  30. 30.What is √1156? =
  31. 31.What is 26²? =
  32. 32.What is 47²? =
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  34. 34.Which of these is a perfect square? (a) 961 (b) 1004 (c) 987
  35. 35.Which of these is a perfect square? (a) 111 (b) 112 (c) 100
  36. 36.A square garden has an area of 576 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 46² and 47²?
  38. 38.A square garden has an area of 1936 square m. How long is each side (in m)?
  39. 39.What is 13²? =
  40. 40.What is the smallest whole number by which 810 must be multiplied to get a perfect square?

Answer key

  1. 1296
  2. 289
  3. 42
  4. 12
  5. 36
  6. 400
  7. 83
  8. 49
  9. 324
  10. 52
  11. 5
  12. 13
  13. 289
  14. 1600
  15. 33
  16. 28
  17. 256
  18. 256
  19. 1089
  20. 784
  21. 576
  22. 74
  23. 11
  24. 2
  25. 361
  26. 6
  27. 5
  28. 21
  29. 2
  30. 34
  31. 676
  32. 2209
  33. 484
  34. 961
  35. 100
  36. 24
  37. 92
  38. 44
  39. 169
  40. 10

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