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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 518 · 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 √8464? =
  2. 2.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 144 square m. How long is each side (in m)?
  4. 4.What is 38²? =
  5. 5.What is √2500? =
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  7. 7.Which of these is a perfect square? (a) 144 (b) 145 (c) 149
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 224 must be divided to get a perfect square?
  11. 11.What is √1089? =
  12. 12.How many whole numbers lie between 30² and 31²?
  13. 13.What is 22²? =
  14. 14.What is √8649? =
  15. 15.What is √2209? =
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √400? =
  18. 18.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  19. 19.Which of these is a perfect square? (a) 1101 (b) 1155 (c) 1089
  20. 20.What is √1849? =
  21. 21.How many whole numbers lie between 33² and 34²?
  22. 22.What is √6400? =
  23. 23.What is 47²? =
  24. 24.Which of these is a perfect square? (a) 782 (b) 729 (c) 731
  25. 25.What is 29²? =
  26. 26.What is 26²? =
  27. 27.A square garden has an area of 1024 square m. How long is each side (in m)?
  28. 28.What is 39²? =
  29. 29.How many whole numbers lie between 27² and 28²?
  30. 30.What is the smallest whole number by which 240 must be divided to get a perfect square?
  31. 31.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 324 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 208 must be divided to get a perfect square?
  34. 34.How many whole numbers lie between 24² and 25²?
  35. 35.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 28 must be divided to get a perfect square?
  37. 37.A square garden has an area of 1225 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 961 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 264 (b) 256 (c) 287
  40. 40.How many whole numbers lie between 8² and 9²?

Answer key

  1. 92
  2. 15
  3. 12
  4. 1444
  5. 50
  6. 256
  7. 144
  8. 784
  9. 196
  10. 14
  11. 33
  12. 60
  13. 484
  14. 93
  15. 47
  16. 169
  17. 20
  18. 14
  19. 1089
  20. 43
  21. 66
  22. 80
  23. 2209
  24. 729
  25. 841
  26. 676
  27. 32
  28. 1521
  29. 54
  30. 15
  31. 676
  32. 18
  33. 13
  34. 48
  35. 13
  36. 7
  37. 35
  38. 31
  39. 256
  40. 16

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