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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 394 · 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 √5329? =
  2. 2.A square garden has an area of 400 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 196 square m. How long is each side (in m)?
  5. 5.What is 55²? =
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  8. 8.How many whole numbers lie between 31² and 32²?
  9. 9.Which of these is a perfect square? (a) 1624 (b) 1643 (c) 1600
  10. 10.Which of these is a perfect square? (a) 824 (b) 784 (c) 821
  11. 11.Which of these is a perfect square? (a) 541 (b) 547 (c) 529
  12. 12.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  13. 13.What is √5929? =
  14. 14.Which of these is a perfect square? (a) 1464 (b) 1444 (c) 1507
  15. 15.What is 31²? =
  16. 16.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 32² and 33²?
  18. 18.What is √625? =
  19. 19.Which of these is a perfect square? (a) 846 (b) 857 (c) 841
  20. 20.What is √1089? =
  21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 20² and 21²?
  23. 23.A square garden has an area of 36 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 13² and 14²?
  28. 28.How many whole numbers lie between 18² and 19²?
  29. 29.How many whole numbers lie between 22² and 23²?
  30. 30.What is √3249? =
  31. 31.What is √3136? =
  32. 32.What is 76²? =
  33. 33.What is the smallest whole number by which 216 must be divided to get a perfect square?
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √8464? =
  36. 36.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  37. 37.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  38. 38.What is √3025? =
  39. 39.What is 74²? =
  40. 40.What is the smallest whole number by which 40 must be multiplied to get a perfect square?

Answer key

  1. 73
  2. 20
  3. 441
  4. 14
  5. 3025
  6. 900
  7. 14
  8. 62
  9. 1600
  10. 784
  11. 529
  12. 7
  13. 77
  14. 1444
  15. 961
  16. 7
  17. 64
  18. 25
  19. 841
  20. 33
  21. 841
  22. 40
  23. 6
  24. 6
  25. 361
  26. 121
  27. 26
  28. 36
  29. 44
  30. 57
  31. 56
  32. 5776
  33. 6
  34. 484
  35. 92
  36. 13
  37. 10
  38. 55
  39. 5476
  40. 10

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