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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 576 · 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 62²? =
  2. 2.Which of these is a perfect square? (a) 224 (b) 221 (c) 196
  3. 3.A square garden has an area of 3025 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 96 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 250 (b) 225 (c) 237
  6. 6.What is the smallest whole number by which 60 must be divided to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 470 (b) 446 (c) 441
  8. 8.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  9. 9.What is 84²? =
  10. 10.A square garden has an area of 1369 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 289 (b) 323 (c) 313
  12. 12.A square garden has an area of 1024 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 245 must be divided to get a perfect square?
  14. 14.How many whole numbers lie between 14² and 15²?
  15. 15.A square garden has an area of 361 square m. How long is each side (in m)?
  16. 16.What is √3721? =
  17. 17.What is 77²? =
  18. 18.Which of these is a perfect square? (a) 1369 (b) 1429 (c) 1391
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 2704 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 729 square m. How long is each side (in m)?
  24. 24.What is √1681? =
  25. 25.What is 85²? =
  26. 26.What is √576? =
  27. 27.How many whole numbers lie between 29² and 30²?
  28. 28.Which of these is a perfect square? (a) 784 (b) 831 (c) 798
  29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √9025? =
  31. 31.How many whole numbers lie between 25² and 26²?
  32. 32.A square garden has an area of 1089 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 20² and 21²?
  34. 34.What is 13²? =
  35. 35.A square garden has an area of 3481 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 33² and 34²?
  38. 38.What is the smallest whole number by which 32 must be divided to get a perfect square?
  39. 39.What is 38²? =
  40. 40.What is √361? =

Answer key

  1. 3844
  2. 196
  3. 55
  4. 6
  5. 225
  6. 15
  7. 441
  8. 10
  9. 7056
  10. 37
  11. 289
  12. 32
  13. 5
  14. 28
  15. 19
  16. 61
  17. 5929
  18. 1369
  19. 25
  20. 6
  21. 52
  22. 6
  23. 27
  24. 41
  25. 7225
  26. 24
  27. 58
  28. 784
  29. 441
  30. 95
  31. 50
  32. 33
  33. 40
  34. 169
  35. 59
  36. 144
  37. 66
  38. 2
  39. 1444
  40. 19

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