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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 85 · 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 √1849? =
  2. 2.What is √7744? =
  3. 3.How many whole numbers lie between 38² and 39²?
  4. 4.What is √6400? =
  5. 5.What is 27²? =
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √784? =
  8. 8.How many whole numbers lie between 19² and 20²?
  9. 9.How many whole numbers lie between 28² and 29²?
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 12 must be divided to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 164 (b) 146 (c) 144
  13. 13.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 121 (b) 143 (c) 122
  15. 15.What is 38²? =
  16. 16.A square garden has an area of 1296 square m. How long is each side (in m)?
  17. 17.What is 41²? =
  18. 18.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  19. 19.What is √2500? =
  20. 20.Which of these is a perfect square? (a) 368 (b) 366 (c) 361
  21. 21.What is 54²? =
  22. 22.Which of these is a perfect square? (a) 331 (b) 324 (c) 333
  23. 23.What is 99²? =
  24. 24.What is √2704? =
  25. 25.How many whole numbers lie between 46² and 47²?
  26. 26.What is √2401? =
  27. 27.Which of these is a perfect square? (a) 441 (b) 445 (c) 454
  28. 28.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 293 (b) 289 (c) 290
  30. 30.What is √7569? =
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 567 must be divided to get a perfect square?
  33. 33.A square garden has an area of 3136 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 1024 square m. How long is each side (in m)?
  36. 36.What is the smallest whole number by which 20 must be divided to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 610 (b) 576 (c) 593
  38. 38.What is √2304? =
  39. 39.What is 97²? =
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 43
  2. 88
  3. 76
  4. 80
  5. 729
  6. 36
  7. 28
  8. 38
  9. 56
  10. 64
  11. 3
  12. 144
  13. 3
  14. 121
  15. 1444
  16. 36
  17. 1681
  18. 3
  19. 50
  20. 361
  21. 2916
  22. 324
  23. 9801
  24. 52
  25. 92
  26. 49
  27. 441
  28. 6
  29. 289
  30. 87
  31. 196
  32. 7
  33. 56
  34. 225
  35. 32
  36. 5
  37. 576
  38. 48
  39. 9409
  40. 100

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