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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 655 · 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 the smallest whole number by which 160 must be divided to get a perfect square?
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √6400? =
  4. 4.What is 95²? =
  5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 1424 (b) 1369 (c) 1384
  7. 7.Which of these is a perfect square? (a) 1543 (b) 1521 (c) 1545
  8. 8.How many whole numbers lie between 34² and 35²?
  9. 9.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 15² and 16²?
  11. 11.What is 69²? =
  12. 12.Which of these is a perfect square? (a) 531 (b) 529 (c) 540
  13. 13.How many whole numbers lie between 7² and 8²?
  14. 14.What is 24²? =
  15. 15.How many whole numbers lie between 12² and 13²?
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  18. 18.Which of these is a perfect square? (a) 375 (b) 386 (c) 361
  19. 19.How many whole numbers lie between 14² and 15²?
  20. 20.What is √3364? =
  21. 21.What is the smallest whole number by which 32 must be divided to get a perfect square?
  22. 22.How many whole numbers lie between 31² and 32²?
  23. 23.What is √7225? =
  24. 24.Which of these is a perfect square? (a) 637 (b) 625 (c) 629
  25. 25.What is √484? =
  26. 26.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  27. 27.How many whole numbers lie between 10² and 11²?
  28. 28.A square garden has an area of 25 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 98 must be divided to get a perfect square?
  30. 30.What is 11²? =
  31. 31.Which of these is a perfect square? (a) 900 (b) 917 (c) 960
  32. 32.A square garden has an area of 81 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 100 square m. How long is each side (in m)?
  34. 34.What is √9409? =
  35. 35.A square garden has an area of 361 square m. How long is each side (in m)?
  36. 36.What is √3721? =
  37. 37.What is 14²? =
  38. 38.A square garden has an area of 196 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 502 (b) 484 (c) 498
  40. 40.What is √6889? =

Answer key

  1. 10
  2. 36
  3. 80
  4. 9025
  5. 59
  6. 1369
  7. 1521
  8. 68
  9. 11
  10. 30
  11. 4761
  12. 529
  13. 14
  14. 576
  15. 24
  16. 100
  17. 121
  18. 361
  19. 28
  20. 58
  21. 2
  22. 62
  23. 85
  24. 625
  25. 22
  26. 7
  27. 20
  28. 5
  29. 2
  30. 121
  31. 900
  32. 9
  33. 10
  34. 97
  35. 19
  36. 61
  37. 196
  38. 14
  39. 484
  40. 83

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