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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 588 · 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 46² and 47²?
  2. 2.What is √841? =
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 26² and 27²?
  5. 5.What is √6400? =
  6. 6.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  7. 7.What is 58²? =
  8. 8.How many whole numbers lie between 13² and 14²?
  9. 9.A square garden has an area of 3136 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 175 must be divided to get a perfect square?
  11. 11.How many whole numbers lie between 16² and 17²?
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.What is √7396? =
  14. 14.Which of these is a perfect square? (a) 529 (b) 530 (c) 548
  15. 15.What is √3969? =
  16. 16.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 955 (b) 903 (c) 900
  18. 18.What is the smallest whole number by which 192 must be divided to get a perfect square?
  19. 19.A square garden has an area of 1849 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 1369 (b) 1440 (c) 1387
  22. 22.How many whole numbers lie between 28² and 29²?
  23. 23.A square garden has an area of 676 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 2916 square m. How long is each side (in m)?
  25. 25.What is 69²? =
  26. 26.A square garden has an area of 484 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 468 (b) 441 (c) 460
  28. 28.What is the smallest whole number by which 147 must be divided to get a perfect square?
  29. 29.What is √1936? =
  30. 30.How many whole numbers lie between 12² and 13²?
  31. 31.Which of these is a perfect square? (a) 150 (b) 144 (c) 162
  32. 32.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  33. 33.What is √8836? =
  34. 34.What is the smallest whole number by which 150 must be divided to get a perfect square?
  35. 35.What is √3721? =
  36. 36.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 867 (b) 894 (c) 841
  40. 40.What is the smallest whole number by which 162 must be multiplied to get a perfect square?

Answer key

  1. 92
  2. 29
  3. 289
  4. 52
  5. 80
  6. 13
  7. 3364
  8. 26
  9. 56
  10. 7
  11. 32
  12. 82
  13. 86
  14. 529
  15. 63
  16. 3
  17. 900
  18. 3
  19. 43
  20. 625
  21. 1369
  22. 56
  23. 26
  24. 54
  25. 4761
  26. 22
  27. 441
  28. 3
  29. 44
  30. 24
  31. 144
  32. 13
  33. 94
  34. 6
  35. 61
  36. 36
  37. 841
  38. 529
  39. 841
  40. 2

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