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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 649 · 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 47² and 48²?
  2. 2.What is √729? =
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 20 must be divided to get a perfect square?
  5. 5.What is the smallest whole number by which 192 must be divided to get a perfect square?
  6. 6.What is 67²? =
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 40 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 18² and 19²?
  10. 10.Which of these is a perfect square? (a) 995 (b) 979 (c) 961
  11. 11.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  12. 12.What is 85²? =
  13. 13.Which of these is a perfect square? (a) 1383 (b) 1421 (c) 1369
  14. 14.What is √5476? =
  15. 15.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  16. 16.What is 19²? =
  17. 17.A square garden has an area of 3600 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 103 (b) 100 (c) 117
  19. 19.A square garden has an area of 1681 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √7921? =
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 50 must be divided to get a perfect square?
  24. 24.A square garden has an area of 900 square m. How long is each side (in m)?
  25. 25.What is √1521? =
  26. 26.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  27. 27.What is the smallest whole number by which 180 must be divided to get a perfect square?
  28. 28.What is 89²? =
  29. 29.Which of these is a perfect square? (a) 257 (b) 256 (c) 282
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √2704? =
  32. 32.How many whole numbers lie between 21² and 22²?
  33. 33.Which of these is a perfect square? (a) 1589 (b) 1530 (c) 1521
  34. 34.What is 49²? =
  35. 35.Which of these is a perfect square? (a) 1163 (b) 1175 (c) 1156
  36. 36.What is 59²? =
  37. 37.Which of these is a perfect square? (a) 1089 (b) 1130 (c) 1139
  38. 38.Which of these is a perfect square? (a) 180 (b) 169 (c) 181
  39. 39.What is √7396? =
  40. 40.How many whole numbers lie between 7² and 8²?

Answer key

  1. 94
  2. 27
  3. 36
  4. 5
  5. 3
  6. 4489
  7. 256
  8. 10
  9. 36
  10. 961
  11. 10
  12. 7225
  13. 1369
  14. 74
  15. 15
  16. 361
  17. 60
  18. 100
  19. 41
  20. 196
  21. 89
  22. 576
  23. 2
  24. 30
  25. 39
  26. 11
  27. 5
  28. 7921
  29. 256
  30. 900
  31. 52
  32. 42
  33. 1521
  34. 2401
  35. 1156
  36. 3481
  37. 1089
  38. 169
  39. 86
  40. 14

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