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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 124 · 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) 757 (b) 735 (c) 729
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 49 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 1655 (b) 1600 (c) 1676
  5. 5.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √121? =
  7. 7.How many whole numbers lie between 41² and 42²?
  8. 8.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 128 must be divided to get a perfect square?
  10. 10.What is √256? =
  11. 11.What is 19²? =
  12. 12.What is the smallest whole number by which 810 must be divided to get a perfect square?
  13. 13.What is √400? =
  14. 14.What is 27²? =
  15. 15.What is 51²? =
  16. 16.Which of these is a perfect square? (a) 407 (b) 400 (c) 429
  17. 17.What is √4761? =
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 216 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 676 (b) 722 (c) 692
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  23. 23.How many whole numbers lie between 45² and 46²?
  24. 24.What is √1369? =
  25. 25.Which of these is a perfect square? (a) 189 (b) 171 (c) 169
  26. 26.A square garden has an area of 3481 square m. How long is each side (in m)?
  27. 27.What is √729? =
  28. 28.What is √361? =
  29. 29.What is 67²? =
  30. 30.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  31. 31.What is 79²? =
  32. 32.How many whole numbers lie between 5² and 6²?
  33. 33.A square garden has an area of 2809 square m. How long is each side (in m)?
  34. 34.What is √2304? =
  35. 35.What is 26²? =
  36. 36.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 990 (b) 961 (c) 964
  38. 38.What is √8464? =
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 48 must be multiplied to get a perfect square?

Answer key

  1. 729
  2. 49
  3. 7
  4. 1600
  5. 729
  6. 11
  7. 82
  8. 13
  9. 2
  10. 16
  11. 361
  12. 10
  13. 20
  14. 729
  15. 2601
  16. 400
  17. 69
  18. 676
  19. 6
  20. 11
  21. 676
  22. 36
  23. 90
  24. 37
  25. 169
  26. 59
  27. 27
  28. 19
  29. 4489
  30. 3
  31. 6241
  32. 10
  33. 53
  34. 48
  35. 676
  36. 2
  37. 961
  38. 92
  39. 225
  40. 3

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