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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 9 · 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.Which of these is a perfect square? (a) 441 (b) 469 (c) 482
  2. 2.What is √1444? =
  3. 3.A square garden has an area of 961 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  5. 5.A square garden has an area of 196 square m. How long is each side (in m)?
  6. 6.What is 47²? =
  7. 7.Which of these is a perfect square? (a) 183 (b) 169 (c) 173
  8. 8.What is √729? =
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √1936? =
  11. 11.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  12. 12.What is 99²? =
  13. 13.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 19² and 20²?
  15. 15.What is √2209? =
  16. 16.What is 38²? =
  17. 17.What is √7921? =
  18. 18.Which of these is a perfect square? (a) 289 (b) 295 (c) 321
  19. 19.How many whole numbers lie between 22² and 23²?
  20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  21. 21.How many whole numbers lie between 7² and 8²?
  22. 22.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 294 must be divided to get a perfect square?
  24. 24.What is 64²? =
  25. 25.A square garden has an area of 2116 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  27. 27.A square garden has an area of 3025 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  29. 29.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  30. 30.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  31. 31.What is √3844? =
  32. 32.What is √4225? =
  33. 33.How many whole numbers lie between 33² and 34²?
  34. 34.What is √6724? =
  35. 35.A square garden has an area of 1296 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 325 (b) 336 (c) 324
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 125 must be divided to get a perfect square?
  39. 39.What is √7225? =
  40. 40.What is √6084? =

Answer key

  1. 441
  2. 38
  3. 31
  4. 11
  5. 14
  6. 2209
  7. 169
  8. 27
  9. 196
  10. 44
  11. 3
  12. 9801
  13. 5
  14. 38
  15. 47
  16. 1444
  17. 89
  18. 289
  19. 44
  20. 64
  21. 14
  22. 6
  23. 6
  24. 4096
  25. 46
  26. 3
  27. 55
  28. 13
  29. 11
  30. 14
  31. 62
  32. 65
  33. 66
  34. 82
  35. 36
  36. 324
  37. 121
  38. 5
  39. 85
  40. 78

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