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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 679 · 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 676 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 1296 (b) 1336 (c) 1366
  3. 3.A square garden has an area of 3136 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 1603 (b) 1625 (c) 1600
  5. 5.What is 63²? =
  6. 6.Which of these is a perfect square? (a) 900 (b) 928 (c) 902
  7. 7.What is √8649? =
  8. 8.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  11. 11.What is √7744? =
  12. 12.What is √256? =
  13. 13.What is √9409? =
  14. 14.What is 36²? =
  15. 15.Which of these is a perfect square? (a) 961 (b) 974 (c) 981
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  18. 18.What is 59²? =
  19. 19.How many whole numbers lie between 24² and 25²?
  20. 20.How many whole numbers lie between 18² and 19²?
  21. 21.What is 88²? =
  22. 22.A square garden has an area of 1681 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 34² and 35²?
  24. 24.Which of these is a perfect square? (a) 289 (b) 320 (c) 305
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 1548 (b) 1521 (c) 1556
  27. 27.How many whole numbers lie between 47² and 48²?
  28. 28.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  29. 29.What is the smallest whole number by which 540 must be divided to get a perfect square?
  30. 30.What is the smallest whole number by which 162 must be divided to get a perfect square?
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 37² and 38²?
  33. 33.What is √1444? =
  34. 34.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  35. 35.What is 12²? =
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 8² and 9²?
  38. 38.What is √1296? =
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is √4096? =

Answer key

  1. 26
  2. 1296
  3. 56
  4. 1600
  5. 3969
  6. 900
  7. 93
  8. 576
  9. 100
  10. 5
  11. 88
  12. 16
  13. 97
  14. 1296
  15. 961
  16. 25
  17. 7
  18. 3481
  19. 48
  20. 36
  21. 7744
  22. 41
  23. 68
  24. 289
  25. 441
  26. 1521
  27. 94
  28. 7
  29. 15
  30. 2
  31. 81
  32. 74
  33. 38
  34. 2
  35. 144
  36. 49
  37. 16
  38. 36
  39. 784
  40. 64

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