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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 696 · 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 361 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 1225 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 384 must be divided to get a perfect square?
  5. 5.What is √441? =
  6. 6.How many whole numbers lie between 21² and 22²?
  7. 7.Which of these is a perfect square? (a) 795 (b) 788 (c) 784
  8. 8.How many whole numbers lie between 24² and 25²?
  9. 9.Which of these is a perfect square? (a) 289 (b) 300 (c) 307
  10. 10.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  11. 11.How many whole numbers lie between 17² and 18²?
  12. 12.What is 77²? =
  13. 13.A square garden has an area of 36 square m. How long is each side (in m)?
  14. 14.What is √2916? =
  15. 15.What is √2209? =
  16. 16.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 16² and 17²?
  18. 18.What is the smallest whole number by which 56 must be divided to get a perfect square?
  19. 19.What is √256? =
  20. 20.A square garden has an area of 2025 square m. How long is each side (in m)?
  21. 21.What is √400? =
  22. 22.How many whole numbers lie between 44² and 45²?
  23. 23.What is 50²? =
  24. 24.What is √4225? =
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √4096? =
  28. 28.A square garden has an area of 1600 square m. How long is each side (in m)?
  29. 29.What is √121? =
  30. 30.What is √6724? =
  31. 31.What is √3136? =
  32. 32.What is 97²? =
  33. 33.What is the smallest whole number by which 891 must be divided to get a perfect square?
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 2916 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 756 (b) 752 (c) 729
  37. 37.What is √1849? =
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the smallest whole number by which 375 must be divided to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 396 (b) 381 (c) 361

Answer key

  1. 19
  2. 81
  3. 35
  4. 6
  5. 21
  6. 42
  7. 784
  8. 48
  9. 289
  10. 10
  11. 34
  12. 5929
  13. 6
  14. 54
  15. 47
  16. 10
  17. 32
  18. 14
  19. 16
  20. 45
  21. 20
  22. 88
  23. 2500
  24. 65
  25. 169
  26. 36
  27. 64
  28. 40
  29. 11
  30. 82
  31. 56
  32. 9409
  33. 11
  34. 400
  35. 54
  36. 729
  37. 43
  38. 576
  39. 15
  40. 361

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