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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 360 · 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.Which of these is a perfect square? (a) 255 (b) 225 (c) 238
  2. 2.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  3. 3.What is √7396? =
  4. 4.A square garden has an area of 1089 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 870 (b) 898 (c) 841
  6. 6.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  7. 7.What is the smallest whole number by which 96 must be divided to get a perfect square?
  8. 8.What is 26²? =
  9. 9.What is 76²? =
  10. 10.What is 13²? =
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 1024 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 149 (b) 144 (c) 156
  14. 14.How many whole numbers lie between 17² and 18²?
  15. 15.What is √784? =
  16. 16.What is √3249? =
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  20. 20.What is √8836? =
  21. 21.What is 46²? =
  22. 22.A square garden has an area of 2209 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 1600 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 1600 (b) 1674 (c) 1619
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  27. 27.What is √9801? =
  28. 28.What is √1681? =
  29. 29.How many whole numbers lie between 32² and 33²?
  30. 30.What is 24²? =
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 1015 (b) 1014 (c) 961
  33. 33.What is 50²? =
  34. 34.How many whole numbers lie between 42² and 43²?
  35. 35.What is 11²? =
  36. 36.What is √2704? =
  37. 37.What is √4356? =
  38. 38.What is √1369? =
  39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 180 must be multiplied to get a perfect square?

Answer key

  1. 225
  2. 3
  3. 86
  4. 33
  5. 841
  6. 2
  7. 6
  8. 676
  9. 5776
  10. 169
  11. 49
  12. 32
  13. 144
  14. 34
  15. 28
  16. 57
  17. 100
  18. 361
  19. 5
  20. 94
  21. 2116
  22. 47
  23. 40
  24. 1600
  25. 484
  26. 6
  27. 99
  28. 41
  29. 64
  30. 576
  31. 196
  32. 961
  33. 2500
  34. 84
  35. 121
  36. 52
  37. 66
  38. 37
  39. 15
  40. 5

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