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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 100 · 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 15² and 16²?
  2. 2.A square garden has an area of 100 square m. How long is each side (in m)?
  3. 3.What is 61²? =
  4. 4.Which of these is a perfect square? (a) 529 (b) 539 (c) 540
  5. 5.How many whole numbers lie between 42² and 43²?
  6. 6.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is 74²? =
  8. 8.Which of these is a perfect square? (a) 1444 (b) 1502 (c) 1487
  9. 9.What is 36²? =
  10. 10.What is the smallest whole number by which 637 must be divided to get a perfect square?
  11. 11.A square garden has an area of 1369 square m. How long is each side (in m)?
  12. 12.What is 97²? =
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  14. 14.A square garden has an area of 625 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 10² and 11²?
  16. 16.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 49 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 448 must be divided to get a perfect square?
  20. 20.A square garden has an area of 64 square m. How long is each side (in m)?
  21. 21.What is √576? =
  22. 22.How many whole numbers lie between 48² and 49²?
  23. 23.How many whole numbers lie between 38² and 39²?
  24. 24.What is the smallest whole number by which 375 must be divided to get a perfect square?
  25. 25.A square garden has an area of 3249 square m. How long is each side (in m)?
  26. 26.What is 62²? =
  27. 27.How many whole numbers lie between 37² and 38²?
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 72²? =
  30. 30.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √1225? =
  33. 33.What is √3969? =
  34. 34.How many whole numbers lie between 5² and 6²?
  35. 35.A square garden has an area of 25 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 18²? =
  38. 38.What is 85²? =
  39. 39.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 52 must be multiplied to get a perfect square?

Answer key

  1. 30
  2. 10
  3. 3721
  4. 529
  5. 84
  6. 784
  7. 5476
  8. 1444
  9. 1296
  10. 13
  11. 37
  12. 9409
  13. 100
  14. 25
  15. 20
  16. 256
  17. 2
  18. 7
  19. 7
  20. 8
  21. 24
  22. 96
  23. 76
  24. 15
  25. 57
  26. 3844
  27. 74
  28. 64
  29. 5184
  30. 11
  31. 484
  32. 35
  33. 63
  34. 10
  35. 5
  36. 81
  37. 324
  38. 7225
  39. 5
  40. 13

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