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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 482 · 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 the smallest whole number by which 245 must be multiplied to get a perfect square?
  2. 2.What is √9604? =
  3. 3.What is √5929? =
  4. 4.A square garden has an area of 900 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 1600 (b) 1671 (c) 1643
  6. 6.How many whole numbers lie between 12² and 13²?
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 825 (b) 784 (c) 805
  9. 9.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  10. 10.What is √3481? =
  11. 11.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 13² and 14²?
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 28² and 29²?
  15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 1024 (b) 1083 (c) 1072
  18. 18.What is √3844? =
  19. 19.A square garden has an area of 100 square m. How long is each side (in m)?
  20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is 68²? =
  22. 22.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  23. 23.What is 24²? =
  24. 24.A square garden has an area of 1600 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 5² and 6²?
  26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 37² and 38²?
  28. 28.How many whole numbers lie between 23² and 24²?
  29. 29.What is 91²? =
  30. 30.What is 82²? =
  31. 31.What is the smallest whole number by which 375 must be divided to get a perfect square?
  32. 32.What is 12²? =
  33. 33.What is √3136? =
  34. 34.A square garden has an area of 1369 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 324 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 17² and 18²?
  37. 37.What is 83²? =
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 38² and 39²?

Answer key

  1. 5
  2. 98
  3. 77
  4. 30
  5. 1600
  6. 24
  7. 441
  8. 784
  9. 10
  10. 59
  11. 14
  12. 26
  13. 196
  14. 56
  15. 729
  16. 900
  17. 1024
  18. 62
  19. 10
  20. 625
  21. 4624
  22. 7
  23. 576
  24. 40
  25. 10
  26. 25
  27. 74
  28. 46
  29. 8281
  30. 6724
  31. 15
  32. 144
  33. 56
  34. 37
  35. 18
  36. 34
  37. 6889
  38. 64
  39. 36
  40. 76

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