← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 681 · 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.A square garden has an area of 225 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 1024 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 100 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 36² and 37²?
  5. 5.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 1369 square m. How long is each side (in m)?
  8. 8.How many whole numbers lie between 12² and 13²?
  9. 9.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  10. 10.What is √3136? =
  11. 11.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  12. 12.What is √6889? =
  13. 13.How many whole numbers lie between 48² and 49²?
  14. 14.How many whole numbers lie between 34² and 35²?
  15. 15.Which of these is a perfect square? (a) 1175 (b) 1207 (c) 1156
  16. 16.How many whole numbers lie between 21² and 22²?
  17. 17.What is √576? =
  18. 18.Which of these is a perfect square? (a) 1521 (b) 1594 (c) 1539
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 1936 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 160 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 124 (b) 121 (c) 131
  23. 23.What is √8281? =
  24. 24.What is 34²? =
  25. 25.A square garden has an area of 441 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 256 (b) 281 (c) 260
  27. 27.What is 38²? =
  28. 28.What is the smallest whole number by which 50 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 44² and 45²?
  30. 30.How many whole numbers lie between 41² and 42²?
  31. 31.What is √1764? =
  32. 32.A square garden has an area of 676 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √2809? =
  36. 36.A square garden has an area of 121 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 397 (b) 371 (c) 361
  38. 38.What is 60²? =
  39. 39.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  40. 40.A square garden has an area of 1444 square m. How long is each side (in m)?

Answer key

  1. 15
  2. 32
  3. 10
  4. 72
  5. 13
  6. 400
  7. 37
  8. 24
  9. 5
  10. 56
  11. 7
  12. 83
  13. 96
  14. 68
  15. 1156
  16. 42
  17. 24
  18. 1521
  19. 36
  20. 44
  21. 10
  22. 121
  23. 91
  24. 1156
  25. 21
  26. 256
  27. 1444
  28. 2
  29. 88
  30. 82
  31. 42
  32. 26
  33. 576
  34. 49
  35. 53
  36. 11
  37. 361
  38. 3600
  39. 5
  40. 38

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