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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 28 · 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.A square garden has an area of 2916 square m. How long is each side (in m)?
  2. 2.What is √3844? =
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 45 must be divided to get a perfect square?
  5. 5.A square garden has an area of 1156 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  7. 7.What is √784? =
  8. 8.What is √6889? =
  9. 9.What is √2601? =
  10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 841 square m. How long is each side (in m)?
  12. 12.What is √2916? =
  13. 13.How many whole numbers lie between 17² and 18²?
  14. 14.A square garden has an area of 3025 square m. How long is each side (in m)?
  15. 15.What is 18²? =
  16. 16.Which of these is a perfect square? (a) 291 (b) 289 (c) 314
  17. 17.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 784 (b) 808 (c) 797
  19. 19.What is the smallest whole number by which 80 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 350 must be divided to get a perfect square?
  21. 21.What is √1936? =
  22. 22.How many whole numbers lie between 8² and 9²?
  23. 23.What is 21²? =
  24. 24.What is the smallest whole number by which 320 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 493 (b) 484 (c) 520
  26. 26.Which of these is a perfect square? (a) 646 (b) 661 (c) 625
  27. 27.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  28. 28.What is the smallest whole number by which 384 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 37² and 38²?
  30. 30.What is 20²? =
  31. 31.Which of these is a perfect square? (a) 934 (b) 958 (c) 900
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 42² and 43²?
  34. 34.What is 87²? =
  35. 35.What is the smallest whole number by which 40 must be divided to get a perfect square?
  36. 36.What is √8281? =
  37. 37.What is 84²? =
  38. 38.What is 48²? =
  39. 39.Which of these is a perfect square? (a) 169 (b) 194 (c) 181
  40. 40.What is 50²? =

Answer key

  1. 54
  2. 62
  3. 196
  4. 5
  5. 34
  6. 15
  7. 28
  8. 83
  9. 51
  10. 361
  11. 29
  12. 54
  13. 34
  14. 55
  15. 324
  16. 289
  17. 7
  18. 784
  19. 5
  20. 14
  21. 44
  22. 16
  23. 441
  24. 5
  25. 484
  26. 625
  27. 3
  28. 6
  29. 74
  30. 400
  31. 900
  32. 144
  33. 84
  34. 7569
  35. 10
  36. 91
  37. 7056
  38. 2304
  39. 169
  40. 2500

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