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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 183 · 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 80 must be multiplied to get a perfect square?
  2. 2.What is 13²? =
  3. 3.What is 92²? =
  4. 4.What is 69²? =
  5. 5.What is the smallest whole number by which 56 must be divided to get a perfect square?
  6. 6.What is 70²? =
  7. 7.How many whole numbers lie between 40² and 41²?
  8. 8.What is 11²? =
  9. 9.What is 96²? =
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √5476? =
  12. 12.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 48²? =
  15. 15.What is the smallest whole number by which 405 must be divided to get a perfect square?
  16. 16.What is √256? =
  17. 17.What is 24²? =
  18. 18.How many whole numbers lie between 37² and 38²?
  19. 19.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 165 (b) 148 (c) 144
  21. 21.What is 12²? =
  22. 22.What is 20²? =
  23. 23.Which of these is a perfect square? (a) 353 (b) 324 (c) 348
  24. 24.A square garden has an area of 961 square m. How long is each side (in m)?
  25. 25.What is √1764? =
  26. 26.A square garden has an area of 2304 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √2601? =
  29. 29.A square garden has an area of 256 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 107 (b) 100 (c) 103
  32. 32.What is the smallest whole number by which 735 must be divided to get a perfect square?
  33. 33.A square garden has an area of 484 square m. How long is each side (in m)?
  34. 34.What is √196? =
  35. 35.How many whole numbers lie between 27² and 28²?
  36. 36.What is 60²? =
  37. 37.A square garden has an area of 121 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 100 square m. How long is each side (in m)?
  39. 39.What is √1521? =
  40. 40.What is 81²? =

Answer key

  1. 5
  2. 169
  3. 8464
  4. 4761
  5. 14
  6. 4900
  7. 80
  8. 121
  9. 9216
  10. 196
  11. 74
  12. 15
  13. 225
  14. 2304
  15. 5
  16. 16
  17. 576
  18. 74
  19. 7
  20. 144
  21. 144
  22. 400
  23. 324
  24. 31
  25. 42
  26. 48
  27. 81
  28. 51
  29. 16
  30. 5
  31. 100
  32. 15
  33. 22
  34. 14
  35. 54
  36. 3600
  37. 11
  38. 10
  39. 39
  40. 6561

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