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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 516 · 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 324 square m. How long is each side (in m)?
  2. 2.What is 42²? =
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 1369 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 256 (b) 281 (c) 287
  7. 7.What is the smallest whole number by which 396 must be divided to get a perfect square?
  8. 8.What is 40²? =
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 181 (b) 169 (c) 183
  11. 11.What is the smallest whole number by which 40 must be divided to get a perfect square?
  12. 12.A square garden has an area of 729 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 1509 (b) 1511 (c) 1444
  14. 14.How many whole numbers lie between 18² and 19²?
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 83²? =
  17. 17.A square garden has an area of 225 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 900 (b) 943 (c) 901
  19. 19.What is √484? =
  20. 20.What is √900? =
  21. 21.What is √2500? =
  22. 22.Which of these is a perfect square? (a) 1175 (b) 1171 (c) 1156
  23. 23.A square garden has an area of 2601 square m. How long is each side (in m)?
  24. 24.What is √1600? =
  25. 25.What is 75²? =
  26. 26.A square garden has an area of 36 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 529 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 625 square m. How long is each side (in m)?
  29. 29.Which of these is a perfect square? (a) 570 (b) 545 (c) 529
  30. 30.What is 13²? =
  31. 31.How many whole numbers lie between 6² and 7²?
  32. 32.What is √8100? =
  33. 33.Which of these is a perfect square? (a) 289 (b) 297 (c) 312
  34. 34.A square garden has an area of 3481 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  36. 36.How many whole numbers lie between 23² and 24²?
  37. 37.Which of these is a perfect square? (a) 963 (b) 961 (c) 972
  38. 38.What is 44²? =
  39. 39.What is √7056? =
  40. 40.Which of these is a perfect square? (a) 137 (b) 130 (c) 121

Answer key

  1. 18
  2. 1764
  3. 36
  4. 100
  5. 37
  6. 256
  7. 11
  8. 1600
  9. 25
  10. 169
  11. 10
  12. 27
  13. 1444
  14. 36
  15. 841
  16. 6889
  17. 15
  18. 900
  19. 22
  20. 30
  21. 50
  22. 1156
  23. 51
  24. 40
  25. 5625
  26. 6
  27. 23
  28. 25
  29. 529
  30. 169
  31. 12
  32. 90
  33. 289
  34. 59
  35. 196
  36. 46
  37. 961
  38. 1936
  39. 84
  40. 121

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