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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 27 · 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 3364 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 804 (b) 784 (c) 819
  3. 3.What is the smallest whole number by which 24 must be divided to get a perfect square?
  4. 4.How many whole numbers lie between 8² and 9²?
  5. 5.What is √2025? =
  6. 6.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  7. 7.What is 93²? =
  8. 8.What is √289? =
  9. 9.Which of these is a perfect square? (a) 694 (b) 676 (c) 711
  10. 10.What is √1521? =
  11. 11.Which of these is a perfect square? (a) 332 (b) 324 (c) 352
  12. 12.A square garden has an area of 1089 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 625 (b) 660 (c) 673
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 30² and 31²?
  16. 16.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 380 (b) 370 (c) 361
  18. 18.What is √169? =
  19. 19.What is √2809? =
  20. 20.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 441 square m. How long is each side (in m)?
  23. 23.What is 41²? =
  24. 24.How many whole numbers lie between 13² and 14²?
  25. 25.Which of these is a perfect square? (a) 208 (b) 196 (c) 199
  26. 26.What is 97²? =
  27. 27.What is the smallest whole number by which 891 must be divided to get a perfect square?
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √4489? =
  30. 30.How many whole numbers lie between 18² and 19²?
  31. 31.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  32. 32.What is 72²? =
  33. 33.Which of these is a perfect square? (a) 453 (b) 441 (c) 480
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 53²? =
  36. 36.Which of these is a perfect square? (a) 433 (b) 411 (c) 400
  37. 37.What is √2401? =
  38. 38.What is 90²? =
  39. 39.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  40. 40.What is 20²? =

Answer key

  1. 58
  2. 784
  3. 6
  4. 16
  5. 45
  6. 3
  7. 8649
  8. 17
  9. 676
  10. 39
  11. 324
  12. 33
  13. 625
  14. 47
  15. 60
  16. 13
  17. 361
  18. 13
  19. 53
  20. 5
  21. 900
  22. 21
  23. 1681
  24. 26
  25. 196
  26. 9409
  27. 11
  28. 64
  29. 67
  30. 36
  31. 10
  32. 5184
  33. 441
  34. 729
  35. 2809
  36. 400
  37. 49
  38. 8100
  39. 11
  40. 400

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