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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 340 · 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) 243 (b) 240 (c) 225
  2. 2.What is 80²? =
  3. 3.What is the smallest whole number by which 375 must be divided to get a perfect square?
  4. 4.How many whole numbers lie between 39² and 40²?
  5. 5.Which of these is a perfect square? (a) 121 (b) 142 (c) 128
  6. 6.What is the smallest whole number by which 60 must be divided to get a perfect square?
  7. 7.What is √900? =
  8. 8.A square garden has an area of 576 square m. How long is each side (in m)?
  9. 9.What is 79²? =
  10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 62²? =
  13. 13.What is √441? =
  14. 14.Which of these is a perfect square? (a) 484 (b) 523 (c) 527
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √400? =
  17. 17.What is the smallest whole number by which 8 must be divided to get a perfect square?
  18. 18.What is √2916? =
  19. 19.How many whole numbers lie between 44² and 45²?
  20. 20.A square garden has an area of 64 square m. How long is each side (in m)?
  21. 21.What is √324? =
  22. 22.Which of these is a perfect square? (a) 1164 (b) 1172 (c) 1156
  23. 23.Which of these is a perfect square? (a) 529 (b) 541 (c) 534
  24. 24.What is the smallest whole number by which 20 must be divided to get a perfect square?
  25. 25.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  26. 26.What is √121? =
  27. 27.Which of these is a perfect square? (a) 100 (b) 114 (c) 111
  28. 28.What is 58²? =
  29. 29.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  30. 30.What is √6889? =
  31. 31.A square garden has an area of 3249 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  33. 33.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 1276 (b) 1293 (c) 1225
  35. 35.How many whole numbers lie between 27² and 28²?
  36. 36.How many whole numbers lie between 5² and 6²?
  37. 37.A square garden has an area of 676 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 1225 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  40. 40.What is 60²? =

Answer key

  1. 225
  2. 6400
  3. 15
  4. 78
  5. 121
  6. 15
  7. 30
  8. 24
  9. 6241
  10. 324
  11. 121
  12. 3844
  13. 21
  14. 484
  15. 400
  16. 20
  17. 2
  18. 54
  19. 88
  20. 8
  21. 18
  22. 1156
  23. 529
  24. 5
  25. 3
  26. 11
  27. 100
  28. 3364
  29. 13
  30. 83
  31. 57
  32. 15
  33. 14
  34. 1225
  35. 54
  36. 10
  37. 26
  38. 35
  39. 6
  40. 3600

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