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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 414 · 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 √625? =
  2. 2.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  3. 3.What is 68²? =
  4. 4.What is 93²? =
  5. 5.What is √4225? =
  6. 6.Which of these is a perfect square? (a) 329 (b) 324 (c) 327
  7. 7.What is 25²? =
  8. 8.What is 56²? =
  9. 9.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 41² and 42²?
  11. 11.A square garden has an area of 1936 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 1089 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 1408 (b) 1378 (c) 1369
  15. 15.Which of these is a perfect square? (a) 255 (b) 244 (c) 225
  16. 16.What is √2025? =
  17. 17.What is √225? =
  18. 18.What is the smallest whole number by which 704 must be divided to get a perfect square?
  19. 19.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 14² and 15²?
  21. 21.Which of these is a perfect square? (a) 1156 (b) 1157 (c) 1172
  22. 22.What is √7744? =
  23. 23.Which of these is a perfect square? (a) 919 (b) 900 (c) 921
  24. 24.What is 88²? =
  25. 25.What is √1024? =
  26. 26.What is √1521? =
  27. 27.Which of these is a perfect square? (a) 125 (b) 142 (c) 121
  28. 28.How many whole numbers lie between 6² and 7²?
  29. 29.What is √1225? =
  30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √484? =
  32. 32.A square garden has an area of 3136 square m. How long is each side (in m)?
  33. 33.What is 20²? =
  34. 34.A square garden has an area of 64 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 53²? =
  37. 37.A square garden has an area of 121 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 324 square m. How long is each side (in m)?
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  40. 40.How many whole numbers lie between 31² and 32²?

Answer key

  1. 25
  2. 13
  3. 4624
  4. 8649
  5. 65
  6. 324
  7. 625
  8. 3136
  9. 6
  10. 82
  11. 44
  12. 784
  13. 33
  14. 1369
  15. 225
  16. 45
  17. 15
  18. 11
  19. 11
  20. 28
  21. 1156
  22. 88
  23. 900
  24. 7744
  25. 32
  26. 39
  27. 121
  28. 12
  29. 35
  30. 576
  31. 22
  32. 56
  33. 400
  34. 8
  35. 324
  36. 2809
  37. 11
  38. 18
  39. 64
  40. 62

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