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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 499 · 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 the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √529? =
  3. 3.What is 67²? =
  4. 4.A square garden has an area of 2401 square m. How long is each side (in m)?
  5. 5.What is √5625? =
  6. 6.A square garden has an area of 961 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 147 must be divided to get a perfect square?
  8. 8.What is 21²? =
  9. 9.What is √1521? =
  10. 10.What is √3249? =
  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 2025 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 784 (b) 839 (c) 827
  14. 14.What is 75²? =
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √841? =
  17. 17.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 169 (b) 184 (c) 192
  19. 19.How many whole numbers lie between 21² and 22²?
  20. 20.Which of these is a perfect square? (a) 606 (b) 583 (c) 576
  21. 21.What is 58²? =
  22. 22.Which of these is a perfect square? (a) 680 (b) 702 (c) 676
  23. 23.What is √1296? =
  24. 24.Which of these is a perfect square? (a) 1428 (b) 1369 (c) 1386
  25. 25.What is 55²? =
  26. 26.What is √9025? =
  27. 27.Which of these is a perfect square? (a) 110 (b) 108 (c) 100
  28. 28.Which of these is a perfect square? (a) 361 (b) 376 (c) 370
  29. 29.How many whole numbers lie between 46² and 47²?
  30. 30.How many whole numbers lie between 25² and 26²?
  31. 31.How many whole numbers lie between 48² and 49²?
  32. 32.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 625 (b) 640 (c) 665
  36. 36.What is 20²? =
  37. 37.What is 18²? =
  38. 38.A square garden has an area of 196 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 18² and 19²?
  40. 40.What is 51²? =

Answer key

  1. 36
  2. 23
  3. 4489
  4. 49
  5. 75
  6. 31
  7. 3
  8. 441
  9. 39
  10. 57
  11. 10
  12. 45
  13. 784
  14. 5625
  15. 169
  16. 29
  17. 11
  18. 169
  19. 42
  20. 576
  21. 3364
  22. 676
  23. 36
  24. 1369
  25. 3025
  26. 95
  27. 100
  28. 361
  29. 92
  30. 50
  31. 96
  32. 2
  33. 729
  34. 3
  35. 625
  36. 400
  37. 324
  38. 14
  39. 36
  40. 2601

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