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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 186 · 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 99 must be multiplied to get a perfect square?
  2. 2.What is 37²? =
  3. 3.A square garden has an area of 3481 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 49² and 50²?
  5. 5.Which of these is a perfect square? (a) 492 (b) 513 (c) 484
  6. 6.Which of these is a perfect square? (a) 1634 (b) 1647 (c) 1600
  7. 7.A square garden has an area of 2209 square m. How long is each side (in m)?
  8. 8.What is √9801? =
  9. 9.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 60 must be divided to get a perfect square?
  11. 11.A square garden has an area of 2304 square m. How long is each side (in m)?
  12. 12.What is 55²? =
  13. 13.What is 68²? =
  14. 14.What is √2601? =
  15. 15.A square garden has an area of 49 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 12² and 13²?
  17. 17.What is the smallest whole number by which 52 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 28 must be divided to get a perfect square?
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 324 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 16² and 17²?
  22. 22.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  23. 23.How many whole numbers lie between 27² and 28²?
  24. 24.What is 81²? =
  25. 25.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √324? =
  27. 27.What is 29²? =
  28. 28.How many whole numbers lie between 15² and 16²?
  29. 29.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  30. 30.What is √1849? =
  31. 31.What is √400? =
  32. 32.What is 13²? =
  33. 33.What is the smallest whole number by which 891 must be divided to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 361 (b) 381 (c) 397
  35. 35.Which of these is a perfect square? (a) 841 (b) 864 (c) 887
  36. 36.Which of these is a perfect square? (a) 927 (b) 923 (c) 900
  37. 37.A square garden has an area of 36 square m. How long is each side (in m)?
  38. 38.What is 27²? =
  39. 39.How many whole numbers lie between 18² and 19²?
  40. 40.How many whole numbers lie between 40² and 41²?

Answer key

  1. 11
  2. 1369
  3. 59
  4. 98
  5. 484
  6. 1600
  7. 47
  8. 99
  9. 900
  10. 15
  11. 48
  12. 3025
  13. 4624
  14. 51
  15. 7
  16. 24
  17. 13
  18. 7
  19. 361
  20. 18
  21. 32
  22. 7
  23. 54
  24. 6561
  25. 841
  26. 18
  27. 841
  28. 30
  29. 13
  30. 43
  31. 20
  32. 169
  33. 11
  34. 361
  35. 841
  36. 900
  37. 6
  38. 729
  39. 36
  40. 80

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