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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 177 · 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.A square garden has an area of 2304 square m. How long is each side (in m)?
  2. 2.What is 59²? =
  3. 3.A square garden has an area of 676 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 432 (b) 401 (c) 400
  5. 5.Which of these is a perfect square? (a) 289 (b) 320 (c) 295
  6. 6.A square garden has an area of 1849 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 441 square m. How long is each side (in m)?
  8. 8.What is 34²? =
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 1225 square m. How long is each side (in m)?
  11. 11.What is √2916? =
  12. 12.A square garden has an area of 529 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 27² and 28²?
  15. 15.What is 78²? =
  16. 16.A square garden has an area of 1521 square m. How long is each side (in m)?
  17. 17.What is 42²? =
  18. 18.Which of these is a perfect square? (a) 151 (b) 144 (c) 146
  19. 19.A square garden has an area of 81 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 896 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 571 (b) 540 (c) 529
  22. 22.What is √5041? =
  23. 23.Which of these is a perfect square? (a) 1458 (b) 1475 (c) 1444
  24. 24.Which of these is a perfect square? (a) 1233 (b) 1287 (c) 1225
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1024 square m. How long is each side (in m)?
  28. 28.What is 46²? =
  29. 29.What is √3600? =
  30. 30.What is 89²? =
  31. 31.A square garden has an area of 961 square m. How long is each side (in m)?
  32. 32.A square garden has an area of 3249 square m. How long is each side (in m)?
  33. 33.What is 62²? =
  34. 34.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 20² and 21²?
  36. 36.What is 53²? =
  37. 37.A square garden has an area of 3136 square m. How long is each side (in m)?
  38. 38.What is √6084? =
  39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 48
  2. 3481
  3. 26
  4. 400
  5. 289
  6. 43
  7. 21
  8. 1156
  9. 361
  10. 35
  11. 54
  12. 23
  13. 15
  14. 54
  15. 6084
  16. 39
  17. 1764
  18. 144
  19. 9
  20. 14
  21. 529
  22. 71
  23. 1444
  24. 1225
  25. 121
  26. 529
  27. 32
  28. 2116
  29. 60
  30. 7921
  31. 31
  32. 57
  33. 3844
  34. 6
  35. 40
  36. 2809
  37. 56
  38. 78
  39. 15
  40. 784

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