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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 91 · 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 √9216? =
  2. 2.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 18² and 19²?
  4. 4.Which of these is a perfect square? (a) 513 (b) 499 (c) 484
  5. 5.Which of these is a perfect square? (a) 724 (b) 689 (c) 676
  6. 6.A square garden has an area of 3249 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  8. 8.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  11. 11.What is 92²? =
  12. 12.How many whole numbers lie between 36² and 37²?
  13. 13.Which of these is a perfect square? (a) 167 (b) 168 (c) 144
  14. 14.What is 36²? =
  15. 15.How many whole numbers lie between 17² and 18²?
  16. 16.Which of these is a perfect square? (a) 652 (b) 662 (c) 625
  17. 17.How many whole numbers lie between 11² and 12²?
  18. 18.What is √2916? =
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 448 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 973 (b) 1006 (c) 961
  22. 22.What is √3136? =
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.Which of these is a perfect square? (a) 1312 (b) 1296 (c) 1336
  25. 25.What is 73²? =
  26. 26.How many whole numbers lie between 10² and 11²?
  27. 27.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  28. 28.What is √1600? =
  29. 29.Which of these is a perfect square? (a) 909 (b) 900 (c) 952
  30. 30.What is 72²? =
  31. 31.What is 27²? =
  32. 32.What is √324? =
  33. 33.What is 17²? =
  34. 34.A square garden has an area of 676 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 5² and 6²?
  36. 36.A square garden has an area of 36 square m. How long is each side (in m)?
  37. 37.A square garden has an area of 1225 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 574 (b) 529 (c) 540
  39. 39.What is √2116? =
  40. 40.What is the smallest whole number by which 56 must be multiplied to get a perfect square?

Answer key

  1. 96
  2. 13
  3. 36
  4. 484
  5. 676
  6. 57
  7. 10
  8. 5
  9. 361
  10. 6
  11. 8464
  12. 72
  13. 144
  14. 1296
  15. 34
  16. 625
  17. 22
  18. 54
  19. 121
  20. 7
  21. 961
  22. 56
  23. 841
  24. 1296
  25. 5329
  26. 20
  27. 10
  28. 40
  29. 900
  30. 5184
  31. 729
  32. 18
  33. 289
  34. 26
  35. 10
  36. 6
  37. 35
  38. 529
  39. 46
  40. 14

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