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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 619 · 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 10 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 181 (b) 169 (c) 192
  3. 3.How many whole numbers lie between 49² and 50²?
  4. 4.What is √8100? =
  5. 5.What is 71²? =
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 24² and 25²?
  8. 8.How many whole numbers lie between 23² and 24²?
  9. 9.How many whole numbers lie between 42² and 43²?
  10. 10.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 1600 (b) 1650 (c) 1621
  13. 13.How many whole numbers lie between 47² and 48²?
  14. 14.Which of these is a perfect square? (a) 441 (b) 453 (c) 450
  15. 15.How many whole numbers lie between 43² and 44²?
  16. 16.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  17. 17.A square garden has an area of 289 square m. How long is each side (in m)?
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 841 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 36² and 37²?
  21. 21.What is the smallest whole number by which 18 must be divided to get a perfect square?
  22. 22.What is the smallest whole number by which 360 must be divided to get a perfect square?
  23. 23.What is 11²? =
  24. 24.A square garden has an area of 36 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 686 must be divided to get a perfect square?
  26. 26.What is √4096? =
  27. 27.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 81 square m. How long is each side (in m)?
  29. 29.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  30. 30.A square garden has an area of 1369 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 407 (b) 400 (c) 411
  32. 32.What is √7744? =
  33. 33.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  34. 34.How many whole numbers lie between 5² and 6²?
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 84²? =
  38. 38.What is √3364? =
  39. 39.What is √529? =
  40. 40.What is the smallest whole number by which 75 must be divided to get a perfect square?

Answer key

  1. 100
  2. 169
  3. 98
  4. 90
  5. 5041
  6. 81
  7. 48
  8. 46
  9. 84
  10. 2
  11. 676
  12. 1600
  13. 94
  14. 441
  15. 86
  16. 14
  17. 17
  18. 361
  19. 29
  20. 72
  21. 2
  22. 10
  23. 121
  24. 6
  25. 14
  26. 64
  27. 49
  28. 9
  29. 15
  30. 37
  31. 400
  32. 88
  33. 6
  34. 10
  35. 441
  36. 625
  37. 7056
  38. 58
  39. 23
  40. 3

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