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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 48 · 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 √5625? =
  2. 2.What is the smallest whole number by which 24 must be divided to get a perfect square?
  3. 3.What is 52²? =
  4. 4.Which of these is a perfect square? (a) 1049 (b) 1084 (c) 1024
  5. 5.A square garden has an area of 441 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 409 (b) 432 (c) 400
  7. 7.What is 43²? =
  8. 8.How many whole numbers lie between 49² and 50²?
  9. 9.Which of these is a perfect square? (a) 1540 (b) 1562 (c) 1521
  10. 10.What is 60²? =
  11. 11.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 50² and 51²?
  13. 13.A square garden has an area of 169 square m. How long is each side (in m)?
  14. 14.What is √4624? =
  15. 15.What is 87²? =
  16. 16.A square garden has an area of 1024 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 1369 (b) 1374 (c) 1420
  18. 18.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  19. 19.Which of these is a perfect square? (a) 150 (b) 159 (c) 144
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  21. 21.How many whole numbers lie between 7² and 8²?
  22. 22.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  24. 24.Which of these is a perfect square? (a) 1136 (b) 1144 (c) 1089
  25. 25.What is the smallest whole number by which 960 must be divided to get a perfect square?
  26. 26.How many whole numbers lie between 31² and 32²?
  27. 27.What is 21²? =
  28. 28.What is √6724? =
  29. 29.What is 16²? =
  30. 30.What is the smallest whole number by which 75 must be divided to get a perfect square?
  31. 31.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 20 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 20² and 21²?
  34. 34.A square garden has an area of 1764 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 198 (b) 209 (c) 196
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is √2025? =
  38. 38.How many whole numbers lie between 46² and 47²?
  39. 39.What is √1024? =
  40. 40.What is the smallest whole number by which 126 must be multiplied to get a perfect square?

Answer key

  1. 75
  2. 6
  3. 2704
  4. 1024
  5. 21
  6. 400
  7. 1849
  8. 98
  9. 1521
  10. 3600
  11. 2
  12. 100
  13. 13
  14. 68
  15. 7569
  16. 32
  17. 1369
  18. 7
  19. 144
  20. 169
  21. 14
  22. 3
  23. 361
  24. 1089
  25. 15
  26. 62
  27. 441
  28. 82
  29. 256
  30. 3
  31. 15
  32. 5
  33. 40
  34. 42
  35. 196
  36. 49
  37. 45
  38. 92
  39. 32
  40. 14

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