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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 481 · 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.Which of these is a perfect square? (a) 900 (b) 930 (c) 912
  2. 2.What is 32²? =
  3. 3.How many whole numbers lie between 15² and 16²?
  4. 4.What is 59²? =
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √2601? =
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √441? =
  9. 9.How many whole numbers lie between 20² and 21²?
  10. 10.What is √1936? =
  11. 11.How many whole numbers lie between 17² and 18²?
  12. 12.What is √2500? =
  13. 13.What is √8649? =
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  16. 16.What is the smallest whole number by which 99 must be divided to get a perfect square?
  17. 17.A square garden has an area of 3600 square m. How long is each side (in m)?
  18. 18.What is √4356? =
  19. 19.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the smallest whole number by which 320 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 824 (b) 784 (c) 787
  23. 23.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 289 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 52 must be divided to get a perfect square?
  27. 27.How many whole numbers lie between 13² and 14²?
  28. 28.What is √6241? =
  29. 29.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  30. 30.Which of these is a perfect square? (a) 274 (b) 259 (c) 256
  31. 31.What is the smallest whole number by which 150 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 1618 (b) 1604 (c) 1600
  33. 33.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  37. 37.What is 79²? =
  38. 38.How many whole numbers lie between 19² and 20²?
  39. 39.How many whole numbers lie between 41² and 42²?
  40. 40.A square garden has an area of 2809 square m. How long is each side (in m)?

Answer key

  1. 900
  2. 1024
  3. 30
  4. 3481
  5. 81
  6. 51
  7. 36
  8. 21
  9. 40
  10. 44
  11. 34
  12. 50
  13. 93
  14. 47
  15. 5
  16. 11
  17. 60
  18. 66
  19. 3
  20. 784
  21. 5
  22. 784
  23. 10
  24. 17
  25. 49
  26. 13
  27. 26
  28. 79
  29. 13
  30. 256
  31. 6
  32. 1600
  33. 6
  34. 256
  35. 729
  36. 13
  37. 6241
  38. 38
  39. 82
  40. 53

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