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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 6 · 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 19 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √7396? =
  3. 3.What is √1225? =
  4. 4.How many whole numbers lie between 19² and 20²?
  5. 5.How many whole numbers lie between 43² and 44²?
  6. 6.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  7. 7.What is 32²? =
  8. 8.What is √4624? =
  9. 9.What is 99²? =
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  12. 12.A square garden has an area of 36 square m. How long is each side (in m)?
  13. 13.What is √400? =
  14. 14.Which of these is a perfect square? (a) 129 (b) 121 (c) 139
  15. 15.How many whole numbers lie between 50² and 51²?
  16. 16.What is the smallest whole number by which 250 must be divided to get a perfect square?
  17. 17.What is √2304? =
  18. 18.What is √7056? =
  19. 19.How many whole numbers lie between 33² and 34²?
  20. 20.A square garden has an area of 3136 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 550 (b) 556 (c) 529
  22. 22.Which of these is a perfect square? (a) 1097 (b) 1154 (c) 1089
  23. 23.A square garden has an area of 1089 square m. How long is each side (in m)?
  24. 24.What is √1156? =
  25. 25.How many whole numbers lie between 48² and 49²?
  26. 26.A square garden has an area of 1369 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √3844? =
  29. 29.Which of these is a perfect square? (a) 1542 (b) 1521 (c) 1534
  30. 30.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √2500? =
  33. 33.A square garden has an area of 1600 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 2209 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 1521 square m. How long is each side (in m)?
  39. 39.What is 48²? =
  40. 40.Which of these is a perfect square? (a) 1515 (b) 1446 (c) 1444

Answer key

  1. 361
  2. 86
  3. 35
  4. 38
  5. 86
  6. 13
  7. 1024
  8. 68
  9. 9801
  10. 256
  11. 196
  12. 6
  13. 20
  14. 121
  15. 100
  16. 10
  17. 48
  18. 84
  19. 66
  20. 56
  21. 529
  22. 1089
  23. 33
  24. 34
  25. 96
  26. 37
  27. 400
  28. 62
  29. 1521
  30. 14
  31. 81
  32. 50
  33. 40
  34. 529
  35. 11
  36. 10
  37. 47
  38. 39
  39. 2304
  40. 1444

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