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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 254 · 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 43² and 44²?
  2. 2.How many whole numbers lie between 8² and 9²?
  3. 3.Which of these is a perfect square? (a) 1096 (b) 1089 (c) 1123
  4. 4.What is √6400? =
  5. 5.What is 83²? =
  6. 6.How many whole numbers lie between 17² and 18²?
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 396 must be divided to get a perfect square?
  10. 10.What is 86²? =
  11. 11.How many whole numbers lie between 50² and 51²?
  12. 12.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  13. 13.What is √121? =
  14. 14.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 31²? =
  16. 16.What is √1764? =
  17. 17.What is 60²? =
  18. 18.What is √2304? =
  19. 19.A square garden has an area of 2025 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 6² and 7²?
  21. 21.What is 79²? =
  22. 22.How many whole numbers lie between 32² and 33²?
  23. 23.How many whole numbers lie between 20² and 21²?
  24. 24.Which of these is a perfect square? (a) 642 (b) 625 (c) 670
  25. 25.A square garden has an area of 3481 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √2916? =
  28. 28.How many whole numbers lie between 36² and 37²?
  29. 29.What is 13²? =
  30. 30.A square garden has an area of 900 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 15² and 16²?
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.What is √5476? =
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  37. 37.What is the smallest whole number by which 126 must be divided to get a perfect square?
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.A square garden has an area of 784 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 320 must be multiplied to get a perfect square?

Answer key

  1. 86
  2. 16
  3. 1089
  4. 80
  5. 6889
  6. 34
  7. 529
  8. 14
  9. 11
  10. 7396
  11. 100
  12. 11
  13. 11
  14. 400
  15. 961
  16. 42
  17. 3600
  18. 48
  19. 45
  20. 12
  21. 6241
  22. 64
  23. 40
  24. 625
  25. 59
  26. 100
  27. 54
  28. 72
  29. 169
  30. 30
  31. 30
  32. 6
  33. 74
  34. 900
  35. 3
  36. 3
  37. 14
  38. 60
  39. 28
  40. 5

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