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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 382 · 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 1849 square m. How long is each side (in m)?
  2. 2.How many whole numbers lie between 10² and 11²?
  3. 3.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 29² and 30²?
  5. 5.What is √4356? =
  6. 6.What is √3600? =
  7. 7.What is 31²? =
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 47²? =
  12. 12.What is √1681? =
  13. 13.Which of these is a perfect square? (a) 563 (b) 529 (c) 570
  14. 14.Which of these is a perfect square? (a) 729 (b) 749 (c) 754
  15. 15.What is √1444? =
  16. 16.How many whole numbers lie between 48² and 49²?
  17. 17.How many whole numbers lie between 24² and 25²?
  18. 18.What is 24²? =
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √576? =
  21. 21.How many whole numbers lie between 46² and 47²?
  22. 22.Which of these is a perfect square? (a) 173 (b) 169 (c) 172
  23. 23.What is √2209? =
  24. 24.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 40²? =
  27. 27.Which of these is a perfect square? (a) 110 (b) 107 (c) 100
  28. 28.Which of these is a perfect square? (a) 1277 (b) 1245 (c) 1225
  29. 29.A square garden has an area of 3364 square m. How long is each side (in m)?
  30. 30.What is 84²? =
  31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 999 (b) 986 (c) 961
  33. 33.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  34. 34.What is √1369? =
  35. 35.What is 14²? =
  36. 36.What is 87²? =
  37. 37.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.What is √1764? =
  40. 40.What is the smallest whole number by which 539 must be multiplied to get a perfect square?

Answer key

  1. 43
  2. 20
  3. 256
  4. 58
  5. 66
  6. 60
  7. 961
  8. 81
  9. 12
  10. 36
  11. 2209
  12. 41
  13. 529
  14. 729
  15. 38
  16. 96
  17. 48
  18. 576
  19. 100
  20. 24
  21. 92
  22. 169
  23. 47
  24. 15
  25. 625
  26. 1600
  27. 100
  28. 1225
  29. 58
  30. 7056
  31. 361
  32. 961
  33. 14
  34. 37
  35. 196
  36. 7569
  37. 13
  38. 60
  39. 42
  40. 11

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