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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 663 · 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 sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 180 must be divided to get a perfect square?
  4. 4.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  5. 5.What is the smallest whole number by which 27 must be divided to get a perfect square?
  6. 6.What is the smallest whole number by which 98 must be divided to get a perfect square?
  7. 7.How many whole numbers lie between 25² and 26²?
  8. 8.A square garden has an area of 529 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 19² and 20²?
  10. 10.A square garden has an area of 961 square m. How long is each side (in m)?
  11. 11.What is √1024? =
  12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is 12²? =
  14. 14.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 47²? =
  17. 17.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  18. 18.A square garden has an area of 289 square m. How long is each side (in m)?
  19. 19.What is 73²? =
  20. 20.What is the smallest whole number by which 539 must be divided to get a perfect square?
  21. 21.What is √1296? =
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 76²? =
  24. 24.Which of these is a perfect square? (a) 1163 (b) 1162 (c) 1156
  25. 25.Which of these is a perfect square? (a) 979 (b) 961 (c) 983
  26. 26.A square garden has an area of 3025 square m. How long is each side (in m)?
  27. 27.What is 26²? =
  28. 28.What is 89²? =
  29. 29.Which of these is a perfect square? (a) 508 (b) 484 (c) 493
  30. 30.What is the smallest whole number by which 112 must be divided to get a perfect square?
  31. 31.What is √1156? =
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.What is 80²? =
  34. 34.What is 72²? =
  35. 35.What is √529? =
  36. 36.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  37. 37.What is the smallest whole number by which 32 must be divided to get a perfect square?
  38. 38.What is √4624? =
  39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 25
  2. 49
  3. 5
  4. 3
  5. 3
  6. 2
  7. 50
  8. 23
  9. 38
  10. 31
  11. 32
  12. 676
  13. 144
  14. 196
  15. 529
  16. 2209
  17. 10
  18. 17
  19. 5329
  20. 11
  21. 36
  22. 121
  23. 5776
  24. 1156
  25. 961
  26. 55
  27. 676
  28. 7921
  29. 484
  30. 7
  31. 34
  32. 6
  33. 6400
  34. 5184
  35. 23
  36. 6
  37. 2
  38. 68
  39. 36
  40. 225

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