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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 200 · 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.How many whole numbers lie between 16² and 17²?
  2. 2.What is √961? =
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 37² and 38²?
  5. 5.A square garden has an area of 1369 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  8. 8.What is 26²? =
  9. 9.What is 36²? =
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 49 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 2916 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 3249 square m. How long is each side (in m)?
  16. 16.What is 37²? =
  17. 17.Which of these is a perfect square? (a) 1306 (b) 1319 (c) 1296
  18. 18.What is 53²? =
  19. 19.What is 38²? =
  20. 20.What is √576? =
  21. 21.How many whole numbers lie between 14² and 15²?
  22. 22.Which of these is a perfect square? (a) 363 (b) 389 (c) 361
  23. 23.What is √225? =
  24. 24.What is √121? =
  25. 25.A square garden has an area of 1156 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 729 (b) 783 (c) 742
  27. 27.What is 31²? =
  28. 28.What is 20²? =
  29. 29.How many whole numbers lie between 43² and 44²?
  30. 30.A square garden has an area of 289 square m. How long is each side (in m)?
  31. 31.What is √3969? =
  32. 32.What is √9025? =
  33. 33.A square garden has an area of 3136 square m. How long is each side (in m)?
  34. 34.What is √2809? =
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  36. 36.A square garden has an area of 900 square m. How long is each side (in m)?
  37. 37.What is √5184? =
  38. 38.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  39. 39.A square garden has an area of 2500 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 27² and 28²?

Answer key

  1. 32
  2. 31
  3. 49
  4. 74
  5. 37
  6. 529
  7. 7
  8. 676
  9. 1296
  10. 676
  11. 841
  12. 729
  13. 7
  14. 54
  15. 57
  16. 1369
  17. 1296
  18. 2809
  19. 1444
  20. 24
  21. 28
  22. 361
  23. 15
  24. 11
  25. 34
  26. 729
  27. 961
  28. 400
  29. 86
  30. 17
  31. 63
  32. 95
  33. 56
  34. 53
  35. 25
  36. 30
  37. 72
  38. 10
  39. 50
  40. 54

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