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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 310 · 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 sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is 55²? =
  3. 3.How many whole numbers lie between 50² and 51²?
  4. 4.What is 95²? =
  5. 5.What is 68²? =
  6. 6.What is 90²? =
  7. 7.What is 63²? =
  8. 8.A square garden has an area of 64 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 539 (b) 529 (c) 535
  10. 10.What is 28²? =
  11. 11.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 5² and 6²?
  13. 13.What is 20²? =
  14. 14.What is 81²? =
  15. 15.What is √4900? =
  16. 16.How many whole numbers lie between 41² and 42²?
  17. 17.What is 14²? =
  18. 18.Which of these is a perfect square? (a) 419 (b) 430 (c) 400
  19. 19.Which of these is a perfect square? (a) 100 (b) 118 (c) 109
  20. 20.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 112 must be divided to get a perfect square?
  22. 22.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
  24. 24.What is 33²? =
  25. 25.Which of these is a perfect square? (a) 1618 (b) 1600 (c) 1620
  26. 26.What is √5476? =
  27. 27.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 97²? =
  29. 29.What is √289? =
  30. 30.What is 92²? =
  31. 31.What is 16²? =
  32. 32.What is the smallest whole number by which 396 must be divided to get a perfect square?
  33. 33.What is 85²? =
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 1764 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1537 (b) 1521 (c) 1552
  37. 37.A square garden has an area of 1156 square m. How long is each side (in m)?
  38. 38.What is 53²? =
  39. 39.How many whole numbers lie between 43² and 44²?
  40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 64
  2. 3025
  3. 100
  4. 9025
  5. 4624
  6. 8100
  7. 3969
  8. 8
  9. 529
  10. 784
  11. 10
  12. 10
  13. 400
  14. 6561
  15. 70
  16. 82
  17. 196
  18. 400
  19. 100
  20. 13
  21. 7
  22. 15
  23. 7
  24. 1089
  25. 1600
  26. 74
  27. 625
  28. 9409
  29. 17
  30. 8464
  31. 256
  32. 11
  33. 7225
  34. 81
  35. 42
  36. 1521
  37. 34
  38. 2809
  39. 86
  40. 25

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