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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 538 · 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.How many whole numbers lie between 6² and 7²?
  2. 2.What is √2116? =
  3. 3.How many whole numbers lie between 16² and 17²?
  4. 4.What is √3600? =
  5. 5.How many whole numbers lie between 24² and 25²?
  6. 6.Which of these is a perfect square? (a) 656 (b) 631 (c) 625
  7. 7.What is the smallest whole number by which 490 must be divided to get a perfect square?
  8. 8.A square garden has an area of 441 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √2601? =
  11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  13. 13.What is √400? =
  14. 14.What is 46²? =
  15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 94²? =
  17. 17.What is √4356? =
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  20. 20.What is √7056? =
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 1024 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 80 must be divided to get a perfect square?
  24. 24.Which of these is a perfect square? (a) 484 (b) 510 (c) 497
  25. 25.What is √4761? =
  26. 26.How many whole numbers lie between 8² and 9²?
  27. 27.A square garden has an area of 2601 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 1089 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 23² and 24²?
  30. 30.What is √8100? =
  31. 31.What is 29²? =
  32. 32.A square garden has an area of 400 square m. How long is each side (in m)?
  33. 33.What is 69²? =
  34. 34.What is √8836? =
  35. 35.What is 17²? =
  36. 36.What is 33²? =
  37. 37.How many whole numbers lie between 9² and 10²?
  38. 38.What is the smallest whole number by which 40 must be divided to get a perfect square?
  39. 39.What is √729? =
  40. 40.How many whole numbers lie between 13² and 14²?

Answer key

  1. 12
  2. 46
  3. 32
  4. 60
  5. 48
  6. 625
  7. 10
  8. 21
  9. 676
  10. 51
  11. 64
  12. 5
  13. 20
  14. 2116
  15. 81
  16. 8836
  17. 66
  18. 361
  19. 2
  20. 84
  21. 25
  22. 32
  23. 5
  24. 484
  25. 69
  26. 16
  27. 51
  28. 33
  29. 46
  30. 90
  31. 841
  32. 20
  33. 4761
  34. 94
  35. 289
  36. 1089
  37. 18
  38. 10
  39. 27
  40. 26

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