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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 72 · 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 97²? =
  2. 2.Which of these is a perfect square? (a) 1261 (b) 1225 (c) 1254
  3. 3.A square garden has an area of 169 square m. How long is each side (in m)?
  4. 4.What is √729? =
  5. 5.What is 25²? =
  6. 6.How many whole numbers lie between 5² and 6²?
  7. 7.A square garden has an area of 196 square m. How long is each side (in m)?
  8. 8.What is 12²? =
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 15²? =
  11. 11.How many whole numbers lie between 16² and 17²?
  12. 12.A square garden has an area of 2916 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 256 square m. How long is each side (in m)?
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 90 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 7² and 8²?
  17. 17.What is √1296? =
  18. 18.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 172 (b) 171 (c) 169
  22. 22.What is √2116? =
  23. 23.A square garden has an area of 1225 square m. How long is each side (in m)?
  24. 24.What is 88²? =
  25. 25.What is the smallest whole number by which 891 must be divided to get a perfect square?
  26. 26.A square garden has an area of 2304 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 46² and 47²?
  28. 28.A square garden has an area of 81 square m. How long is each side (in m)?
  29. 29.What is √3249? =
  30. 30.What is 47²? =
  31. 31.How many whole numbers lie between 33² and 34²?
  32. 32.What is √1600? =
  33. 33.What is 23²? =
  34. 34.How many whole numbers lie between 8² and 9²?
  35. 35.A square garden has an area of 3249 square m. How long is each side (in m)?
  36. 36.What is 51²? =
  37. 37.What is √841? =
  38. 38.A square garden has an area of 121 square m. How long is each side (in m)?
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  40. 40.Which of these is a perfect square? (a) 259 (b) 278 (c) 256

Answer key

  1. 9409
  2. 1225
  3. 13
  4. 27
  5. 625
  6. 10
  7. 14
  8. 144
  9. 196
  10. 225
  11. 32
  12. 54
  13. 16
  14. 576
  15. 10
  16. 14
  17. 36
  18. 11
  19. 36
  20. 15
  21. 169
  22. 46
  23. 35
  24. 7744
  25. 11
  26. 48
  27. 92
  28. 9
  29. 57
  30. 2209
  31. 66
  32. 40
  33. 529
  34. 16
  35. 57
  36. 2601
  37. 29
  38. 11
  39. 729
  40. 256

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