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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 625 · 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.How many whole numbers lie between 27² and 28²?
  2. 2.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 436 (b) 400 (c) 439
  5. 5.What is the smallest whole number by which 80 must be divided to get a perfect square?
  6. 6.A square garden has an area of 144 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 980 (b) 961 (c) 1010
  8. 8.What is √4096? =
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 557 (b) 535 (c) 529
  11. 11.Which of these is a perfect square? (a) 484 (b) 490 (c) 502
  12. 12.How many whole numbers lie between 17² and 18²?
  13. 13.How many whole numbers lie between 13² and 14²?
  14. 14.How many whole numbers lie between 47² and 48²?
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 100 (b) 103 (c) 111
  17. 17.What is √1156? =
  18. 18.What is 87²? =
  19. 19.A square garden has an area of 1600 square m. How long is each side (in m)?
  20. 20.What is 50²? =
  21. 21.Which of these is a perfect square? (a) 764 (b) 774 (c) 729
  22. 22.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 185 (b) 175 (c) 169
  24. 24.What is √5625? =
  25. 25.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1156 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 36²? =
  30. 30.What is 99²? =
  31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 896 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  34. 34.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 88²? =
  36. 36.Which of these is a perfect square? (a) 1336 (b) 1330 (c) 1296
  37. 37.What is √784? =
  38. 38.What is 69²? =
  39. 39.How many whole numbers lie between 30² and 31²?
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 54
  2. 676
  3. 900
  4. 400
  5. 5
  6. 12
  7. 961
  8. 64
  9. 169
  10. 529
  11. 484
  12. 34
  13. 26
  14. 94
  15. 36
  16. 100
  17. 34
  18. 7569
  19. 40
  20. 2500
  21. 729
  22. 14
  23. 169
  24. 75
  25. 15
  26. 81
  27. 34
  28. 529
  29. 1296
  30. 9801
  31. 441
  32. 14
  33. 7
  34. 324
  35. 7744
  36. 1296
  37. 28
  38. 4761
  39. 60
  40. 784

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