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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 282 · 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) 1600 (b) 1669 (c) 1617
  2. 2.Which of these is a perfect square? (a) 126 (b) 121 (c) 140
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 949 (b) 913 (c) 900
  5. 5.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 164 (b) 144 (c) 145
  7. 7.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  10. 10.How many whole numbers lie between 41² and 42²?
  11. 11.How many whole numbers lie between 8² and 9²?
  12. 12.How many whole numbers lie between 27² and 28²?
  13. 13.A square garden has an area of 441 square m. How long is each side (in m)?
  14. 14.What is 65²? =
  15. 15.What is √196? =
  16. 16.What is √576? =
  17. 17.Which of these is a perfect square? (a) 790 (b) 784 (c) 785
  18. 18.What is √169? =
  19. 19.What is 83²? =
  20. 20.A square garden has an area of 2809 square m. How long is each side (in m)?
  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 256 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √3481? =
  25. 25.A square garden has an area of 64 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1225 (b) 1231 (c) 1271
  27. 27.What is the smallest whole number by which 540 must be divided to get a perfect square?
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 72²? =
  30. 30.A square garden has an area of 484 square m. How long is each side (in m)?
  31. 31.What is 94²? =
  32. 32.What is the smallest whole number by which 72 must be divided to get a perfect square?
  33. 33.What is 25²? =
  34. 34.How many whole numbers lie between 35² and 36²?
  35. 35.What is √2704? =
  36. 36.What is 56²? =
  37. 37.What is 96²? =
  38. 38.What is the smallest whole number by which 8 must be divided to get a perfect square?
  39. 39.How many whole numbers lie between 45² and 46²?
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 1600
  2. 121
  3. 196
  4. 900
  5. 10
  6. 144
  7. 10
  8. 144
  9. 484
  10. 82
  11. 16
  12. 54
  13. 21
  14. 4225
  15. 14
  16. 24
  17. 784
  18. 13
  19. 6889
  20. 53
  21. 3
  22. 16
  23. 100
  24. 59
  25. 8
  26. 1225
  27. 15
  28. 49
  29. 5184
  30. 22
  31. 8836
  32. 2
  33. 625
  34. 70
  35. 52
  36. 3136
  37. 9216
  38. 2
  39. 90
  40. 121

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