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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 132 · 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 486 must be multiplied to get a perfect square?
  2. 2.A square garden has an area of 144 square m. How long is each side (in m)?
  3. 3.What is 80²? =
  4. 4.What is 70²? =
  5. 5.What is √3364? =
  6. 6.How many whole numbers lie between 17² and 18²?
  7. 7.What is 78²? =
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 14² and 15²?
  10. 10.How many whole numbers lie between 9² and 10²?
  11. 11.What is √1764? =
  12. 12.What is 52²? =
  13. 13.What is 67²? =
  14. 14.What is √484? =
  15. 15.What is √441? =
  16. 16.What is √1681? =
  17. 17.A square garden has an area of 676 square m. How long is each side (in m)?
  18. 18.What is 61²? =
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 81 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 117 must be divided to get a perfect square?
  22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 19²? =
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √144? =
  26. 26.Which of these is a perfect square? (a) 1369 (b) 1372 (c) 1380
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 49 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 1600 square m. How long is each side (in m)?
  30. 30.What is √9025? =
  31. 31.A square garden has an area of 576 square m. How long is each side (in m)?
  32. 32.What is 59²? =
  33. 33.What is 53²? =
  34. 34.What is 17²? =
  35. 35.What is √3721? =
  36. 36.What is √5776? =
  37. 37.What is √2704? =
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 92²? =
  40. 40.How many whole numbers lie between 29² and 30²?

Answer key

  1. 6
  2. 12
  3. 6400
  4. 4900
  5. 58
  6. 34
  7. 6084
  8. 100
  9. 28
  10. 18
  11. 42
  12. 2704
  13. 4489
  14. 22
  15. 21
  16. 41
  17. 26
  18. 3721
  19. 484
  20. 9
  21. 13
  22. 441
  23. 361
  24. 529
  25. 12
  26. 1369
  27. 49
  28. 7
  29. 40
  30. 95
  31. 24
  32. 3481
  33. 2809
  34. 289
  35. 61
  36. 76
  37. 52
  38. 144
  39. 8464
  40. 58

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