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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 84 · 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 8² and 9²?
  2. 2.What is 80²? =
  3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √8836? =
  5. 5.A square garden has an area of 3136 square m. How long is each side (in m)?
  6. 6.What is √3025? =
  7. 7.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  8. 8.A square garden has an area of 2809 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 99²? =
  12. 12.What is √196? =
  13. 13.Which of these is a perfect square? (a) 1312 (b) 1305 (c) 1296
  14. 14.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  15. 15.How many whole numbers lie between 17² and 18²?
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 633 (b) 636 (c) 625
  18. 18.What is √3136? =
  19. 19.What is the smallest whole number by which 125 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 8 must be divided to get a perfect square?
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √3249? =
  24. 24.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 729 (b) 772 (c) 771
  26. 26.A square garden has an area of 225 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 1681 square m. How long is each side (in m)?
  28. 28.What is √729? =
  29. 29.What is the smallest whole number by which 243 must be divided to get a perfect square?
  30. 30.A square garden has an area of 529 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 19² and 20²?
  32. 32.What is √2209? =
  33. 33.How many whole numbers lie between 46² and 47²?
  34. 34.How many whole numbers lie between 30² and 31²?
  35. 35.A square garden has an area of 441 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 81 square m. How long is each side (in m)?
  37. 37.What is 52²? =
  38. 38.What is √324? =
  39. 39.What is the smallest whole number by which 216 must be divided to get a perfect square?
  40. 40.What is 19²? =

Answer key

  1. 16
  2. 6400
  3. 576
  4. 94
  5. 56
  6. 55
  7. 196
  8. 53
  9. 100
  10. 25
  11. 9801
  12. 14
  13. 1296
  14. 5
  15. 34
  16. 81
  17. 625
  18. 56
  19. 5
  20. 2
  21. 64
  22. 169
  23. 57
  24. 7
  25. 729
  26. 15
  27. 41
  28. 27
  29. 3
  30. 23
  31. 38
  32. 47
  33. 92
  34. 60
  35. 21
  36. 9
  37. 2704
  38. 18
  39. 6
  40. 361

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