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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 152 · 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 162 must be multiplied to get a perfect square?
  2. 2.Which of these is a perfect square? (a) 346 (b) 337 (c) 324
  3. 3.What is 56²? =
  4. 4.How many whole numbers lie between 19² and 20²?
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  7. 7.What is the smallest whole number by which 12 must be divided to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 1540 (b) 1526 (c) 1521
  9. 9.What is 49²? =
  10. 10.How many whole numbers lie between 31² and 32²?
  11. 11.How many whole numbers lie between 29² and 30²?
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.How many whole numbers lie between 11² and 12²?
  14. 14.What is √784? =
  15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the smallest whole number by which 245 must be divided to get a perfect square?
  17. 17.A square garden has an area of 441 square m. How long is each side (in m)?
  18. 18.A square garden has an area of 1296 square m. How long is each side (in m)?
  19. 19.What is 29²? =
  20. 20.What is 73²? =
  21. 21.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  22. 22.A square garden has an area of 625 square m. How long is each side (in m)?
  23. 23.What is 71²? =
  24. 24.How many whole numbers lie between 24² and 25²?
  25. 25.A square garden has an area of 3364 square m. How long is each side (in m)?
  26. 26.What is √1296? =
  27. 27.How many whole numbers lie between 13² and 14²?
  28. 28.Which of these is a perfect square? (a) 295 (b) 322 (c) 289
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 35²? =
  31. 31.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  32. 32.What is 41²? =
  33. 33.What is 13²? =
  34. 34.What is √7921? =
  35. 35.What is √1089? =
  36. 36.What is √729? =
  37. 37.What is 81²? =
  38. 38.What is √6724? =
  39. 39.What is 15²? =
  40. 40.What is √4761? =

Answer key

  1. 2
  2. 324
  3. 3136
  4. 38
  5. 100
  6. 7
  7. 3
  8. 1521
  9. 2401
  10. 62
  11. 58
  12. 82
  13. 22
  14. 28
  15. 289
  16. 5
  17. 21
  18. 36
  19. 841
  20. 5329
  21. 3
  22. 25
  23. 5041
  24. 48
  25. 58
  26. 36
  27. 26
  28. 289
  29. 196
  30. 1225
  31. 3
  32. 1681
  33. 169
  34. 89
  35. 33
  36. 27
  37. 6561
  38. 82
  39. 225
  40. 69

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