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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 164 · 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 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is 35²? =
  4. 4.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 18² and 19²?
  6. 6.What is the smallest whole number by which 245 must be divided to get a perfect square?
  7. 7.A square garden has an area of 1600 square m. How long is each side (in m)?
  8. 8.What is 89²? =
  9. 9.What is √5929? =
  10. 10.What is √4761? =
  11. 11.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 256 square m. How long is each side (in m)?
  13. 13.What is √3136? =
  14. 14.A square garden has an area of 49 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 324 (b) 347 (c) 336
  16. 16.What is √2916? =
  17. 17.What is the smallest whole number by which 640 must be divided to get a perfect square?
  18. 18.How many whole numbers lie between 19² and 20²?
  19. 19.A square garden has an area of 36 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  21. 21.What is 80²? =
  22. 22.How many whole numbers lie between 24² and 25²?
  23. 23.A square garden has an area of 1089 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 1396 (b) 1381 (c) 1369
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 361 (b) 370 (c) 362
  27. 27.A square garden has an area of 1764 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 3364 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 50² and 51²?
  30. 30.A square garden has an area of 2916 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 229 (b) 225 (c) 227
  32. 32.What is √289? =
  33. 33.Which of these is a perfect square? (a) 1454 (b) 1467 (c) 1444
  34. 34.Which of these is a perfect square? (a) 289 (b) 306 (c) 314
  35. 35.What is √6084? =
  36. 36.What is the smallest whole number by which 20 must be divided to get a perfect square?
  37. 37.What is 15²? =
  38. 38.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 196 (b) 204 (c) 199
  40. 40.What is the smallest whole number by which 117 must be multiplied to get a perfect square?

Answer key

  1. 36
  2. 324
  3. 1225
  4. 14
  5. 36
  6. 5
  7. 40
  8. 7921
  9. 77
  10. 69
  11. 6
  12. 16
  13. 56
  14. 7
  15. 324
  16. 54
  17. 10
  18. 38
  19. 6
  20. 5
  21. 6400
  22. 48
  23. 33
  24. 1369
  25. 169
  26. 361
  27. 42
  28. 58
  29. 100
  30. 54
  31. 225
  32. 17
  33. 1444
  34. 289
  35. 78
  36. 5
  37. 225
  38. 6
  39. 196
  40. 13

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