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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 172 · 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 63 must be divided to get a perfect square?
  2. 2.What is 48²? =
  3. 3.What is √1225? =
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 13² and 14²?
  6. 6.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  7. 7.What is √144? =
  8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 264 (b) 256 (c) 258
  11. 11.A square garden has an area of 1444 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 27² and 28²?
  13. 13.What is 20²? =
  14. 14.Which of these is a perfect square? (a) 1130 (b) 1100 (c) 1089
  15. 15.A square garden has an area of 2401 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 2209 square m. How long is each side (in m)?
  17. 17.What is √5184? =
  18. 18.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  19. 19.What is 94²? =
  20. 20.What is √2500? =
  21. 21.How many whole numbers lie between 6² and 7²?
  22. 22.What is 21²? =
  23. 23.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  24. 24.What is 77²? =
  25. 25.Which of these is a perfect square? (a) 289 (b) 317 (c) 308
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √2601? =
  28. 28.What is the smallest whole number by which 160 must be divided to get a perfect square?
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 7² and 8²?
  32. 32.What is √7744? =
  33. 33.Which of these is a perfect square? (a) 749 (b) 729 (c) 780
  34. 34.Which of these is a perfect square? (a) 1256 (b) 1242 (c) 1225
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is √961? =
  37. 37.How many whole numbers lie between 33² and 34²?
  38. 38.Which of these is a perfect square? (a) 881 (b) 841 (c) 858
  39. 39.What is √625? =
  40. 40.What is the smallest whole number by which 468 must be multiplied to get a perfect square?

Answer key

  1. 7
  2. 2304
  3. 35
  4. 64
  5. 26
  6. 7
  7. 12
  8. 625
  9. 256
  10. 256
  11. 38
  12. 54
  13. 400
  14. 1089
  15. 49
  16. 47
  17. 72
  18. 15
  19. 8836
  20. 50
  21. 12
  22. 441
  23. 7
  24. 5929
  25. 289
  26. 324
  27. 51
  28. 10
  29. 576
  30. 2
  31. 14
  32. 88
  33. 729
  34. 1225
  35. 441
  36. 31
  37. 66
  38. 841
  39. 25
  40. 13

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