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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 176 · 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 20 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √4356? =
  3. 3.How many whole numbers lie between 20² and 21²?
  4. 4.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 16² and 17²?
  6. 6.Which of these is a perfect square? (a) 1662 (b) 1675 (c) 1600
  7. 7.Which of these is a perfect square? (a) 505 (b) 495 (c) 484
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 80²? =
  11. 11.Which of these is a perfect square? (a) 1041 (b) 1075 (c) 1024
  12. 12.Which of these is a perfect square? (a) 876 (b) 841 (c) 881
  13. 13.What is 16²? =
  14. 14.How many whole numbers lie between 19² and 20²?
  15. 15.Which of these is a perfect square? (a) 729 (b) 746 (c) 743
  16. 16.A square garden has an area of 3481 square m. How long is each side (in m)?
  17. 17.What is √9801? =
  18. 18.How many whole numbers lie between 14² and 15²?
  19. 19.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  20. 20.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 1089 (b) 1112 (c) 1147
  22. 22.A square garden has an area of 784 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 225 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 324 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1521 square m. How long is each side (in m)?
  28. 28.What is 49²? =
  29. 29.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  30. 30.What is 63²? =
  31. 31.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 256 (b) 263 (c) 286
  33. 33.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 2401 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 169 (b) 174 (c) 192
  37. 37.What is 41²? =
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 289 (b) 314 (c) 318
  40. 40.Which of these is a perfect square? (a) 820 (b) 807 (c) 784

Answer key

  1. 400
  2. 66
  3. 40
  4. 14
  5. 32
  6. 1600
  7. 484
  8. 576
  9. 100
  10. 6400
  11. 1024
  12. 841
  13. 256
  14. 38
  15. 729
  16. 59
  17. 99
  18. 28
  19. 7
  20. 2
  21. 1089
  22. 28
  23. 2
  24. 15
  25. 18
  26. 81
  27. 39
  28. 2401
  29. 6
  30. 3969
  31. 5
  32. 256
  33. 10
  34. 484
  35. 49
  36. 169
  37. 1681
  38. 784
  39. 289
  40. 784

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