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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 118 · 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 √1444? =
  2. 2.What is √6400? =
  3. 3.Which of these is a perfect square? (a) 682 (b) 725 (c) 676
  4. 4.How many whole numbers lie between 22² and 23²?
  5. 5.A square garden has an area of 1296 square m. How long is each side (in m)?
  6. 6.What is 21²? =
  7. 7.What is the smallest whole number by which 20 must be divided to get a perfect square?
  8. 8.What is √1225? =
  9. 9.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 20² and 21²?
  12. 12.What is √9409? =
  13. 13.What is the smallest whole number by which 350 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 1272 (b) 1225 (c) 1260
  15. 15.A square garden has an area of 1600 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 36 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 781 (b) 749 (c) 729
  18. 18.How many whole numbers lie between 29² and 30²?
  19. 19.What is 66²? =
  20. 20.What is √3481? =
  21. 21.What is 98²? =
  22. 22.What is the smallest whole number by which 891 must be divided to get a perfect square?
  23. 23.What is 20²? =
  24. 24.How many whole numbers lie between 37² and 38²?
  25. 25.How many whole numbers lie between 47² and 48²?
  26. 26.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 121 (b) 136 (c) 143
  28. 28.Which of these is a perfect square? (a) 404 (b) 400 (c) 413
  29. 29.What is √1936? =
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 468 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 375 must be divided to get a perfect square?
  34. 34.What is √7744? =
  35. 35.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  36. 36.A square garden has an area of 361 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 171 (b) 173 (c) 169
  38. 38.What is √1156? =
  39. 39.What is √1024? =
  40. 40.What is the smallest whole number by which 8 must be divided to get a perfect square?

Answer key

  1. 38
  2. 80
  3. 676
  4. 44
  5. 36
  6. 441
  7. 5
  8. 35
  9. 2
  10. 289
  11. 40
  12. 97
  13. 14
  14. 1225
  15. 40
  16. 6
  17. 729
  18. 58
  19. 4356
  20. 59
  21. 9604
  22. 11
  23. 400
  24. 74
  25. 94
  26. 11
  27. 121
  28. 400
  29. 44
  30. 81
  31. 121
  32. 13
  33. 15
  34. 88
  35. 5
  36. 19
  37. 169
  38. 34
  39. 32
  40. 2

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