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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 140 · 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 245 must be multiplied to get a perfect square?
  2. 2.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  3. 3.What is √7225? =
  4. 4.What is 43²? =
  5. 5.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √961? =
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 196 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 26² and 27²?
  11. 11.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  12. 12.What is √2916? =
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the smallest whole number by which 704 must be divided to get a perfect square?
  15. 15.What is √1369? =
  16. 16.A square garden has an area of 289 square m. How long is each side (in m)?
  17. 17.What is 51²? =
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1329 (b) 1296 (c) 1300
  20. 20.What is 75²? =
  21. 21.A square garden has an area of 144 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 225 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  24. 24.What is 50²? =
  25. 25.What is √324? =
  26. 26.Which of these is a perfect square? (a) 134 (b) 133 (c) 121
  27. 27.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 36 square m. How long is each side (in m)?
  30. 30.What is √4356? =
  31. 31.How many whole numbers lie between 8² and 9²?
  32. 32.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 256 (b) 284 (c) 270
  34. 34.A square garden has an area of 361 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 1225 square m. How long is each side (in m)?
  36. 36.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  37. 37.What is √5929? =
  38. 38.A square garden has an area of 3136 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 21² and 22²?

Answer key

  1. 5
  2. 2
  3. 85
  4. 1849
  5. 625
  6. 289
  7. 31
  8. 121
  9. 14
  10. 52
  11. 7
  12. 54
  13. 196
  14. 11
  15. 37
  16. 17
  17. 2601
  18. 441
  19. 1296
  20. 5625
  21. 12
  22. 15
  23. 5
  24. 2500
  25. 18
  26. 121
  27. 169
  28. 900
  29. 6
  30. 66
  31. 16
  32. 10
  33. 256
  34. 19
  35. 35
  36. 3
  37. 77
  38. 56
  39. 5
  40. 42

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