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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 255 · 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 smallest whole number by which 1053 must be multiplied to get a perfect square?
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 1369 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 144 (b) 167 (c) 145
  5. 5.Which of these is a perfect square? (a) 282 (b) 256 (c) 270
  6. 6.What is √8100? =
  7. 7.What is √4489? =
  8. 8.What is √7744? =
  9. 9.How many whole numbers lie between 17² and 18²?
  10. 10.A square garden has an area of 400 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 298 (b) 289 (c) 300
  12. 12.What is 22²? =
  13. 13.What is 35²? =
  14. 14.What is the smallest whole number by which 32 must be divided to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 335 (b) 357 (c) 324
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 44² and 45²?
  18. 18.What is 75²? =
  19. 19.What is the smallest whole number by which 175 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 2601 square m. How long is each side (in m)?
  23. 23.What is √3136? =
  24. 24.What is √9409? =
  25. 25.Which of these is a perfect square? (a) 972 (b) 980 (c) 961
  26. 26.A square garden has an area of 64 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 5² and 6²?
  28. 28.What is √2809? =
  29. 29.A square garden has an area of 3600 square m. How long is each side (in m)?
  30. 30.What is √5329? =
  31. 31.A square garden has an area of 1764 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 16² and 17²?
  33. 33.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 176 must be divided to get a perfect square?
  35. 35.What is 23²? =
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 1348 (b) 1316 (c) 1296
  39. 39.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  40. 40.What is 96²? =

Answer key

  1. 13
  2. 169
  3. 37
  4. 144
  5. 256
  6. 90
  7. 67
  8. 88
  9. 34
  10. 20
  11. 289
  12. 484
  13. 1225
  14. 2
  15. 324
  16. 900
  17. 88
  18. 5625
  19. 7
  20. 15
  21. 64
  22. 51
  23. 56
  24. 97
  25. 961
  26. 8
  27. 10
  28. 53
  29. 60
  30. 73
  31. 42
  32. 32
  33. 5
  34. 11
  35. 529
  36. 49
  37. 225
  38. 1296
  39. 15
  40. 9216

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