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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 336 · 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.Which of these is a perfect square? (a) 764 (b) 735 (c) 729
  2. 2.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 86²? =
  4. 4.How many whole numbers lie between 34² and 35²?
  5. 5.What is 20²? =
  6. 6.What is √256? =
  7. 7.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  8. 8.How many whole numbers lie between 16² and 17²?
  9. 9.A square garden has an area of 1600 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 1570 (b) 1521 (c) 1538
  12. 12.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  13. 13.A square garden has an area of 2304 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 869 (b) 885 (c) 841
  15. 15.A square garden has an area of 25 square m. How long is each side (in m)?
  16. 16.What is √6400? =
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 54 must be divided to get a perfect square?
  19. 19.Which of these is a perfect square? (a) 1401 (b) 1387 (c) 1369
  20. 20.What is √676? =
  21. 21.A square garden has an area of 529 square m. How long is each side (in m)?
  22. 22.What is 26²? =
  23. 23.What is the smallest whole number by which 117 must be divided to get a perfect square?
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 66²? =
  26. 26.Which of these is a perfect square? (a) 576 (b) 613 (c) 610
  27. 27.A square garden has an area of 3249 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √4225? =
  30. 30.What is 80²? =
  31. 31.Which of these is a perfect square? (a) 447 (b) 441 (c) 463
  32. 32.Which of these is a perfect square? (a) 784 (b) 825 (c) 805
  33. 33.Which of these is a perfect square? (a) 144 (b) 162 (c) 160
  34. 34.What is 39²? =
  35. 35.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  36. 36.What is √1849? =
  37. 37.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √3025? =
  40. 40.Which of these is a perfect square? (a) 1252 (b) 1225 (c) 1238

Answer key

  1. 729
  2. 529
  3. 7396
  4. 68
  5. 400
  6. 16
  7. 6
  8. 32
  9. 40
  10. 10
  11. 1521
  12. 3
  13. 48
  14. 841
  15. 5
  16. 80
  17. 121
  18. 6
  19. 1369
  20. 26
  21. 23
  22. 676
  23. 13
  24. 36
  25. 4356
  26. 576
  27. 57
  28. 576
  29. 65
  30. 6400
  31. 441
  32. 784
  33. 144
  34. 1521
  35. 15
  36. 43
  37. 100
  38. 900
  39. 55
  40. 1225

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