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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 427 · 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.How many whole numbers lie between 38² and 39²?
  2. 2.What is √225? =
  3. 3.Which of these is a perfect square? (a) 256 (b) 260 (c) 270
  4. 4.How many whole numbers lie between 43² and 44²?
  5. 5.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 31² and 32²?
  9. 9.Which of these is a perfect square? (a) 1466 (b) 1488 (c) 1444
  10. 10.What is 28²? =
  11. 11.What is √8100? =
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √6084? =
  14. 14.Which of these is a perfect square? (a) 1379 (b) 1371 (c) 1369
  15. 15.What is √729? =
  16. 16.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  17. 17.What is √4225? =
  18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 332 (b) 356 (c) 324
  20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  21. 21.A square garden has an area of 2601 square m. How long is each side (in m)?
  22. 22.What is 62²? =
  23. 23.A square garden has an area of 2916 square m. How long is each side (in m)?
  24. 24.What is 26²? =
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 361 square m. How long is each side (in m)?
  27. 27.What is √1521? =
  28. 28.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  29. 29.How many whole numbers lie between 14² and 15²?
  30. 30.A square garden has an area of 3600 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 400 square m. How long is each side (in m)?
  32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is √7921? =
  34. 34.What is √900? =
  35. 35.What is 44²? =
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 216 must be divided to get a perfect square?
  38. 38.What is 69²? =
  39. 39.How many whole numbers lie between 8² and 9²?
  40. 40.What is 65²? =

Answer key

  1. 76
  2. 15
  3. 256
  4. 86
  5. 13
  6. 841
  7. 256
  8. 62
  9. 1444
  10. 784
  11. 90
  12. 121
  13. 78
  14. 1369
  15. 27
  16. 2
  17. 65
  18. 144
  19. 324
  20. 900
  21. 51
  22. 3844
  23. 54
  24. 676
  25. 81
  26. 19
  27. 39
  28. 15
  29. 28
  30. 60
  31. 20
  32. 576
  33. 89
  34. 30
  35. 1936
  36. 361
  37. 6
  38. 4761
  39. 16
  40. 4225

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