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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 51 · 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.A square garden has an area of 3600 square m. How long is each side (in m)?
  2. 2.What is √9409? =
  3. 3.What is √400? =
  4. 4.What is 66²? =
  5. 5.How many whole numbers lie between 18² and 19²?
  6. 6.How many whole numbers lie between 39² and 40²?
  7. 7.What is √2304? =
  8. 8.A square garden has an area of 100 square m. How long is each side (in m)?
  9. 9.What is 15²? =
  10. 10.What is √5184? =
  11. 11.How many whole numbers lie between 50² and 51²?
  12. 12.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  13. 13.What is √2500? =
  14. 14.What is √9216? =
  15. 15.A square garden has an area of 2209 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 1547 (b) 1583 (c) 1521
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √1089? =
  19. 19.What is 48²? =
  20. 20.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  21. 21.What is 18²? =
  22. 22.What is 99²? =
  23. 23.How many whole numbers lie between 12² and 13²?
  24. 24.What is 43²? =
  25. 25.A square garden has an area of 400 square m. How long is each side (in m)?
  26. 26.What is √625? =
  27. 27.Which of these is a perfect square? (a) 404 (b) 400 (c) 440
  28. 28.How many whole numbers lie between 42² and 43²?
  29. 29.What is 74²? =
  30. 30.What is √4225? =
  31. 31.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  32. 32.What is 47²? =
  33. 33.What is √961? =
  34. 34.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 8² and 9²?
  36. 36.Which of these is a perfect square? (a) 484 (b) 485 (c) 506
  37. 37.What is the smallest whole number by which 175 must be divided to get a perfect square?
  38. 38.What is 30²? =
  39. 39.How many whole numbers lie between 25² and 26²?
  40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 60
  2. 97
  3. 20
  4. 4356
  5. 36
  6. 78
  7. 48
  8. 10
  9. 225
  10. 72
  11. 100
  12. 13
  13. 50
  14. 96
  15. 47
  16. 1521
  17. 289
  18. 33
  19. 2304
  20. 14
  21. 324
  22. 9801
  23. 24
  24. 1849
  25. 20
  26. 25
  27. 400
  28. 84
  29. 5476
  30. 65
  31. 3
  32. 2209
  33. 31
  34. 6
  35. 16
  36. 484
  37. 7
  38. 900
  39. 50
  40. 144

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