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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 274 · 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 √3136? =
  2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 320 must be divided to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 529 (b) 567 (c) 548
  5. 5.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  6. 6.What is the smallest whole number by which 350 must be divided to get a perfect square?
  7. 7.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  8. 8.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  9. 9.A square garden has an area of 3136 square m. How long is each side (in m)?
  10. 10.What is 21²? =
  11. 11.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 23² and 24²?
  13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  14. 14.Which of these is a perfect square? (a) 237 (b) 225 (c) 248
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is 20²? =
  17. 17.A square garden has an area of 2601 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 582 (b) 576 (c) 578
  19. 19.What is √196? =
  20. 20.What is √9604? =
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 12² and 13²?
  25. 25.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 35² and 36²?
  28. 28.What is √6084? =
  29. 29.What is √225? =
  30. 30.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 39² and 40²?
  32. 32.Which of these is a perfect square? (a) 1376 (b) 1402 (c) 1369
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 18² and 19²?
  35. 35.What is the smallest whole number by which 490 must be divided to get a perfect square?
  36. 36.What is 94²? =
  37. 37.What is √2304? =
  38. 38.How many whole numbers lie between 21² and 22²?
  39. 39.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  40. 40.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 56
  2. 400
  3. 5
  4. 529
  5. 15
  6. 14
  7. 5
  8. 14
  9. 56
  10. 441
  11. 2
  12. 46
  13. 784
  14. 225
  15. 64
  16. 400
  17. 51
  18. 576
  19. 14
  20. 98
  21. 121
  22. 484
  23. 324
  24. 24
  25. 7
  26. 144
  27. 70
  28. 78
  29. 15
  30. 2
  31. 78
  32. 1369
  33. 625
  34. 36
  35. 10
  36. 8836
  37. 48
  38. 42
  39. 5
  40. 196

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