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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 372 · 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 34²? =
  2. 2.Which of these is a perfect square? (a) 513 (b) 484 (c) 491
  3. 3.A square garden has an area of 2809 square m. How long is each side (in m)?
  4. 4.What is √5329? =
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the smallest whole number by which 405 must be divided to get a perfect square?
  7. 7.What is 82²? =
  8. 8.What is 78²? =
  9. 9.Which of these is a perfect square? (a) 478 (b) 441 (c) 455
  10. 10.How many whole numbers lie between 27² and 28²?
  11. 11.What is √256? =
  12. 12.What is 75²? =
  13. 13.Which of these is a perfect square? (a) 1548 (b) 1521 (c) 1560
  14. 14.What is 90²? =
  15. 15.Which of these is a perfect square? (a) 1613 (b) 1645 (c) 1600
  16. 16.A square garden has an area of 625 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 100 square m. How long is each side (in m)?
  19. 19.What is √7396? =
  20. 20.What is 59²? =
  21. 21.What is √784? =
  22. 22.How many whole numbers lie between 37² and 38²?
  23. 23.A square garden has an area of 1089 square m. How long is each side (in m)?
  24. 24.How many whole numbers lie between 48² and 49²?
  25. 25.What is 26²? =
  26. 26.What is 23²? =
  27. 27.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  28. 28.A square garden has an area of 289 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 21² and 22²?
  30. 30.How many whole numbers lie between 5² and 6²?
  31. 31.Which of these is a perfect square? (a) 143 (b) 121 (c) 125
  32. 32.What is 41²? =
  33. 33.A square garden has an area of 841 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √169? =
  36. 36.Which of these is a perfect square? (a) 576 (b) 612 (c) 603
  37. 37.What is 65²? =
  38. 38.Which of these is a perfect square? (a) 144 (b) 147 (c) 165
  39. 39.How many whole numbers lie between 10² and 11²?
  40. 40.What is the smallest whole number by which 735 must be multiplied to get a perfect square?

Answer key

  1. 1156
  2. 484
  3. 53
  4. 73
  5. 100
  6. 5
  7. 6724
  8. 6084
  9. 441
  10. 54
  11. 16
  12. 5625
  13. 1521
  14. 8100
  15. 1600
  16. 25
  17. 256
  18. 10
  19. 86
  20. 3481
  21. 28
  22. 74
  23. 33
  24. 96
  25. 676
  26. 529
  27. 10
  28. 17
  29. 42
  30. 10
  31. 121
  32. 1681
  33. 29
  34. 361
  35. 13
  36. 576
  37. 4225
  38. 144
  39. 20
  40. 15

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