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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 560 · 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.How many whole numbers lie between 43² and 44²?
  2. 2.What is the smallest whole number by which 63 must be divided to get a perfect square?
  3. 3.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  4. 4.What is √256? =
  5. 5.Which of these is a perfect square? (a) 740 (b) 745 (c) 729
  6. 6.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  7. 7.What is √1936? =
  8. 8.Which of these is a perfect square? (a) 108 (b) 114 (c) 100
  9. 9.What is 62²? =
  10. 10.What is 51²? =
  11. 11.How many whole numbers lie between 21² and 22²?
  12. 12.What is √6889? =
  13. 13.A square garden has an area of 25 square m. How long is each side (in m)?
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 8² and 9²?
  16. 16.What is √2601? =
  17. 17.What is 13²? =
  18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  20. 20.What is the smallest whole number by which 960 must be divided to get a perfect square?
  21. 21.What is the smallest whole number by which 360 must be divided to get a perfect square?
  22. 22.A square garden has an area of 1156 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 56²? =
  25. 25.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  27. 27.What is √841? =
  28. 28.A square garden has an area of 1764 square m. How long is each side (in m)?
  29. 29.What is √576? =
  30. 30.What is √5476? =
  31. 31.What is √8836? =
  32. 32.How many whole numbers lie between 20² and 21²?
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 46² and 47²?
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 1585 (b) 1551 (c) 1521
  37. 37.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
  38. 38.What is 80²? =
  39. 39.A square garden has an area of 841 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 225 square m. How long is each side (in m)?

Answer key

  1. 86
  2. 7
  3. 7
  4. 16
  5. 729
  6. 2
  7. 44
  8. 100
  9. 3844
  10. 2601
  11. 42
  12. 83
  13. 5
  14. 64
  15. 16
  16. 51
  17. 169
  18. 169
  19. 5
  20. 15
  21. 10
  22. 34
  23. 196
  24. 3136
  25. 7
  26. 5
  27. 29
  28. 42
  29. 24
  30. 74
  31. 94
  32. 40
  33. 49
  34. 92
  35. 529
  36. 1521
  37. 13
  38. 6400
  39. 29
  40. 15

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