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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 5 · 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 the smallest whole number by which 486 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 40 must be divided to get a perfect square?
  3. 3.A square garden has an area of 1444 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 1288 (b) 1225 (c) 1228
  5. 5.Which of these is a perfect square? (a) 1003 (b) 963 (c) 961
  6. 6.What is 71²? =
  7. 7.What is √1024? =
  8. 8.A square garden has an area of 3364 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  10. 10.A square garden has an area of 2601 square m. How long is each side (in m)?
  11. 11.A square garden has an area of 3025 square m. How long is each side (in m)?
  12. 12.What is 19²? =
  13. 13.What is 44²? =
  14. 14.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  15. 15.How many whole numbers lie between 50² and 51²?
  16. 16.What is 34²? =
  17. 17.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  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) 1325 (b) 1303 (c) 1296
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 41²? =
  24. 24.How many whole numbers lie between 15² and 16²?
  25. 25.Which of these is a perfect square? (a) 223 (b) 222 (c) 196
  26. 26.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 651 (b) 672 (c) 625
  28. 28.Which of these is a perfect square? (a) 237 (b) 233 (c) 225
  29. 29.What is √1444? =
  30. 30.Which of these is a perfect square? (a) 1369 (b) 1380 (c) 1418
  31. 31.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 95²? =
  33. 33.What is √5476? =
  34. 34.What is 15²? =
  35. 35.How many whole numbers lie between 6² and 7²?
  36. 36.How many whole numbers lie between 27² and 28²?
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √4624? =
  39. 39.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  40. 40.A square garden has an area of 2116 square m. How long is each side (in m)?

Answer key

  1. 6
  2. 10
  3. 38
  4. 1225
  5. 961
  6. 5041
  7. 32
  8. 58
  9. 6
  10. 51
  11. 55
  12. 361
  13. 1936
  14. 7
  15. 100
  16. 1156
  17. 13
  18. 256
  19. 1296
  20. 169
  21. 64
  22. 441
  23. 1681
  24. 30
  25. 196
  26. 2
  27. 625
  28. 225
  29. 38
  30. 1369
  31. 289
  32. 9025
  33. 74
  34. 225
  35. 12
  36. 54
  37. 729
  38. 68
  39. 15
  40. 46

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