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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 165 · 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 90²? =
  2. 2.A square garden has an area of 121 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 2601 square m. How long is each side (in m)?
  4. 4.How many whole numbers lie between 31² and 32²?
  5. 5.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  6. 6.What is 71²? =
  7. 7.What is √9025? =
  8. 8.What is 67²? =
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √1296? =
  12. 12.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  13. 13.How many whole numbers lie between 22² and 23²?
  14. 14.What is 59²? =
  15. 15.What is the smallest whole number by which 704 must be divided to get a perfect square?
  16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 17² and 18²?
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1417 (b) 1391 (c) 1369
  20. 20.A square garden has an area of 2209 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 20² and 21²?
  22. 22.What is √3481? =
  23. 23.What is the smallest whole number by which 180 must be divided to get a perfect square?
  24. 24.How many whole numbers lie between 7² and 8²?
  25. 25.What is √9604? =
  26. 26.What is √6084? =
  27. 27.Which of these is a perfect square? (a) 740 (b) 729 (c) 782
  28. 28.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 1019 (b) 985 (c) 961
  30. 30.How many whole numbers lie between 23² and 24²?
  31. 31.What is √3136? =
  32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 18² and 19²?
  35. 35.What is the smallest whole number by which 490 must be divided to get a perfect square?
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 97²? =
  38. 38.What is √576? =
  39. 39.A square garden has an area of 100 square m. How long is each side (in m)?
  40. 40.What is √1764? =

Answer key

  1. 8100
  2. 11
  3. 51
  4. 62
  5. 13
  6. 5041
  7. 95
  8. 4489
  9. 64
  10. 361
  11. 36
  12. 5
  13. 44
  14. 3481
  15. 11
  16. 289
  17. 34
  18. 49
  19. 1369
  20. 47
  21. 40
  22. 59
  23. 5
  24. 14
  25. 98
  26. 78
  27. 729
  28. 6
  29. 961
  30. 46
  31. 56
  32. 36
  33. 484
  34. 36
  35. 10
  36. 441
  37. 9409
  38. 24
  39. 10
  40. 42

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