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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 606 · 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 √1089? =
  2. 2.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 73²? =
  5. 5.What is √256? =
  6. 6.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  7. 7.What is √5476? =
  8. 8.What is √729? =
  9. 9.A square garden has an area of 1296 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 180 must be divided to get a perfect square?
  14. 14.What is 78²? =
  15. 15.Which of these is a perfect square? (a) 1491 (b) 1500 (c) 1444
  16. 16.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 50² and 51²?
  18. 18.What is √2500? =
  19. 19.What is √2704? =
  20. 20.What is √1849? =
  21. 21.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  22. 22.What is 14²? =
  23. 23.What is 56²? =
  24. 24.What is 28²? =
  25. 25.What is √6400? =
  26. 26.A square garden has an area of 64 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  29. 29.What is √1444? =
  30. 30.What is √5929? =
  31. 31.Which of these is a perfect square? (a) 481 (b) 441 (c) 483
  32. 32.What is 22²? =
  33. 33.Which of these is a perfect square? (a) 379 (b) 361 (c) 384
  34. 34.What is the smallest whole number by which 150 must be divided to get a perfect square?
  35. 35.A square garden has an area of 256 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 282 (b) 276 (c) 256
  37. 37.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 20² and 21²?
  39. 39.How many whole numbers lie between 18² and 19²?
  40. 40.Which of these is a perfect square? (a) 901 (b) 900 (c) 915

Answer key

  1. 33
  2. 13
  3. 81
  4. 5329
  5. 16
  6. 6
  7. 74
  8. 27
  9. 36
  10. 484
  11. 5
  12. 289
  13. 5
  14. 6084
  15. 1444
  16. 3
  17. 100
  18. 50
  19. 52
  20. 43
  21. 7
  22. 196
  23. 3136
  24. 784
  25. 80
  26. 8
  27. 49
  28. 15
  29. 38
  30. 77
  31. 441
  32. 484
  33. 361
  34. 6
  35. 16
  36. 256
  37. 529
  38. 40
  39. 36
  40. 900

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