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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 19 · 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 26² and 27²?
  2. 2.What is the smallest whole number by which 640 must be divided to get a perfect square?
  3. 3.A square garden has an area of 1521 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  5. 5.A square garden has an area of 1225 square m. How long is each side (in m)?
  6. 6.What is √6889? =
  7. 7.How many whole numbers lie between 38² and 39²?
  8. 8.What is the smallest whole number by which 486 must be divided to get a perfect square?
  9. 9.A square garden has an area of 676 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 25² and 26²?
  12. 12.What is 15²? =
  13. 13.A square garden has an area of 3481 square m. How long is each side (in m)?
  14. 14.What is 34²? =
  15. 15.What is 98²? =
  16. 16.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  17. 17.A square garden has an area of 289 square m. How long is each side (in m)?
  18. 18.What is √6241? =
  19. 19.A square garden has an area of 2025 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √256? =
  22. 22.What is √7744? =
  23. 23.What is 81²? =
  24. 24.Which of these is a perfect square? (a) 1576 (b) 1521 (c) 1546
  25. 25.What is 75²? =
  26. 26.What is √289? =
  27. 27.Which of these is a perfect square? (a) 161 (b) 145 (c) 144
  28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 18² and 19²?
  30. 30.What is √3136? =
  31. 31.What is 12²? =
  32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is 43²? =
  34. 34.How many whole numbers lie between 11² and 12²?
  35. 35.How many whole numbers lie between 16² and 17²?
  36. 36.What is √5476? =
  37. 37.Which of these is a perfect square? (a) 719 (b) 677 (c) 676
  38. 38.What is 62²? =
  39. 39.A square garden has an area of 3364 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 1156 square m. How long is each side (in m)?

Answer key

  1. 52
  2. 10
  3. 39
  4. 10
  5. 35
  6. 83
  7. 76
  8. 6
  9. 26
  10. 196
  11. 50
  12. 225
  13. 59
  14. 1156
  15. 9604
  16. 11
  17. 17
  18. 79
  19. 45
  20. 36
  21. 16
  22. 88
  23. 6561
  24. 1521
  25. 5625
  26. 17
  27. 144
  28. 225
  29. 36
  30. 56
  31. 144
  32. 441
  33. 1849
  34. 22
  35. 32
  36. 74
  37. 676
  38. 3844
  39. 58
  40. 34

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