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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 467 · 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 sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √484? =
  3. 3.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  4. 4.What is 27²? =
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 3481 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 676 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 1658 (b) 1600 (c) 1678
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 63 must be divided to get a perfect square?
  11. 11.What is √8100? =
  12. 12.Which of these is a perfect square? (a) 1056 (b) 1024 (c) 1065
  13. 13.Which of these is a perfect square? (a) 910 (b) 907 (c) 900
  14. 14.What is 60²? =
  15. 15.How many whole numbers lie between 19² and 20²?
  16. 16.What is the smallest whole number by which 320 must be divided to get a perfect square?
  17. 17.What is 80²? =
  18. 18.Which of these is a perfect square? (a) 215 (b) 223 (c) 196
  19. 19.What is the smallest whole number by which 243 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  21. 21.How many whole numbers lie between 22² and 23²?
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √7921? =
  24. 24.What is √1089? =
  25. 25.What is 50²? =
  26. 26.What is 83²? =
  27. 27.A square garden has an area of 400 square m. How long is each side (in m)?
  28. 28.What is √4489? =
  29. 29.How many whole numbers lie between 44² and 45²?
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 81²? =
  32. 32.How many whole numbers lie between 23² and 24²?
  33. 33.A square garden has an area of 2500 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 396 must be divided to get a perfect square?
  35. 35.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 69²? =
  38. 38.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  39. 39.A square garden has an area of 3600 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 169 square m. How long is each side (in m)?

Answer key

  1. 324
  2. 22
  3. 10
  4. 729
  5. 361
  6. 59
  7. 26
  8. 1600
  9. 576
  10. 7
  11. 90
  12. 1024
  13. 900
  14. 3600
  15. 38
  16. 5
  17. 6400
  18. 196
  19. 3
  20. 5
  21. 44
  22. 400
  23. 89
  24. 33
  25. 2500
  26. 6889
  27. 20
  28. 67
  29. 88
  30. 225
  31. 6561
  32. 46
  33. 50
  34. 11
  35. 729
  36. 484
  37. 4761
  38. 15
  39. 60
  40. 13

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