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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 297 · 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) 1609 (b) 1600 (c) 1604
  2. 2.How many whole numbers lie between 30² and 31²?
  3. 3.What is 27²? =
  4. 4.How many whole numbers lie between 8² and 9²?
  5. 5.What is √6400? =
  6. 6.Which of these is a perfect square? (a) 194 (b) 180 (c) 169
  7. 7.What is the smallest whole number by which 44 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 343 must be divided to get a perfect square?
  9. 9.What is √2809? =
  10. 10.What is 32²? =
  11. 11.Which of these is a perfect square? (a) 961 (b) 1010 (c) 1000
  12. 12.Which of these is a perfect square? (a) 816 (b) 784 (c) 790
  13. 13.What is 62²? =
  14. 14.How many whole numbers lie between 5² and 6²?
  15. 15.What is √529? =
  16. 16.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  17. 17.What is 40²? =
  18. 18.How many whole numbers lie between 10² and 11²?
  19. 19.What is 29²? =
  20. 20.A square garden has an area of 2704 square m. How long is each side (in m)?
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √784? =
  23. 23.A square garden has an area of 529 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 1216 (b) 1210 (c) 1156
  25. 25.What is 87²? =
  26. 26.What is 34²? =
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the smallest whole number by which 52 must be divided to get a perfect square?
  29. 29.What is 78²? =
  30. 30.How many whole numbers lie between 27² and 28²?
  31. 31.How many whole numbers lie between 50² and 51²?
  32. 32.A square garden has an area of 3481 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 2116 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 124 (b) 142 (c) 121
  35. 35.What is the smallest whole number by which 176 must be divided to get a perfect square?
  36. 36.A square garden has an area of 361 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  38. 38.What is the smallest whole number by which 539 must be divided to get a perfect square?
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 1600
  2. 60
  3. 729
  4. 16
  5. 80
  6. 169
  7. 11
  8. 7
  9. 53
  10. 1024
  11. 961
  12. 784
  13. 3844
  14. 10
  15. 23
  16. 2
  17. 1600
  18. 20
  19. 841
  20. 52
  21. 36
  22. 28
  23. 23
  24. 1156
  25. 7569
  26. 1156
  27. 25
  28. 13
  29. 6084
  30. 54
  31. 100
  32. 59
  33. 46
  34. 121
  35. 11
  36. 19
  37. 3
  38. 11
  39. 784
  40. 676

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