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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 487 · 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.What is the smallest whole number by which 128 must be divided to get a perfect square?
  2. 2.What is √2601? =
  3. 3.What is 80²? =
  4. 4.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 46² and 47²?
  6. 6.What is √1369? =
  7. 7.A square garden has an area of 400 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 961 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 160 must be divided to get a perfect square?
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 35²? =
  13. 13.A square garden has an area of 1369 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 196 (b) 219 (c) 197
  15. 15.Which of these is a perfect square? (a) 806 (b) 784 (c) 810
  16. 16.What is 39²? =
  17. 17.How many whole numbers lie between 16² and 17²?
  18. 18.What is √6724? =
  19. 19.Which of these is a perfect square? (a) 100 (b) 108 (c) 109
  20. 20.What is √529? =
  21. 21.What is 53²? =
  22. 22.Which of these is a perfect square? (a) 141 (b) 129 (c) 121
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √3721? =
  25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 64 square m. How long is each side (in m)?
  27. 27.What is √2025? =
  28. 28.What is the smallest whole number by which 162 must be divided to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 430 (b) 400 (c) 402
  30. 30.What is 33²? =
  31. 31.What is √6889? =
  32. 32.What is the smallest whole number by which 80 must be divided to get a perfect square?
  33. 33.What is √144? =
  34. 34.How many whole numbers lie between 9² and 10²?
  35. 35.Which of these is a perfect square? (a) 739 (b) 760 (c) 729
  36. 36.How many whole numbers lie between 12² and 13²?
  37. 37.What is √7921? =
  38. 38.What is the smallest whole number by which 896 must be divided to get a perfect square?
  39. 39.What is √9604? =
  40. 40.What is √784? =

Answer key

  1. 2
  2. 51
  3. 6400
  4. 2
  5. 92
  6. 37
  7. 20
  8. 31
  9. 10
  10. 196
  11. 484
  12. 1225
  13. 37
  14. 196
  15. 784
  16. 1521
  17. 32
  18. 82
  19. 100
  20. 23
  21. 2809
  22. 121
  23. 625
  24. 61
  25. 144
  26. 8
  27. 45
  28. 2
  29. 400
  30. 1089
  31. 83
  32. 5
  33. 12
  34. 18
  35. 729
  36. 24
  37. 89
  38. 14
  39. 98
  40. 28

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