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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 718 · 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 34² and 35²?
  2. 2.A square garden has an area of 361 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √484? =
  5. 5.Which of these is a perfect square? (a) 1187 (b) 1204 (c) 1156
  6. 6.How many whole numbers lie between 50² and 51²?
  7. 7.A square garden has an area of 625 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 240 must be divided to get a perfect square?
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 484 square m. How long is each side (in m)?
  11. 11.What is √3364? =
  12. 12.A square garden has an area of 1156 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 1032 (b) 1028 (c) 1024
  15. 15.Which of these is a perfect square? (a) 100 (b) 115 (c) 109
  16. 16.What is 92²? =
  17. 17.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 36²? =
  20. 20.A square garden has an area of 256 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 33² and 34²?
  22. 22.What is 18²? =
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √2704? =
  25. 25.What is √729? =
  26. 26.How many whole numbers lie between 28² and 29²?
  27. 27.Which of these is a perfect square? (a) 848 (b) 892 (c) 841
  28. 28.What is √121? =
  29. 29.What is 15²? =
  30. 30.A square garden has an area of 1444 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 41² and 42²?
  33. 33.Which of these is a perfect square? (a) 1268 (b) 1232 (c) 1225
  34. 34.How many whole numbers lie between 17² and 18²?
  35. 35.Which of these is a perfect square? (a) 138 (b) 130 (c) 121
  36. 36.What is √400? =
  37. 37.What is 64²? =
  38. 38.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  39. 39.What is √8281? =
  40. 40.What is the smallest whole number by which 891 must be divided to get a perfect square?

Answer key

  1. 68
  2. 19
  3. 25
  4. 22
  5. 1156
  6. 100
  7. 25
  8. 15
  9. 400
  10. 22
  11. 58
  12. 34
  13. 7
  14. 1024
  15. 100
  16. 8464
  17. 3
  18. 256
  19. 1296
  20. 16
  21. 66
  22. 324
  23. 225
  24. 52
  25. 27
  26. 56
  27. 841
  28. 11
  29. 225
  30. 38
  31. 576
  32. 82
  33. 1225
  34. 34
  35. 121
  36. 20
  37. 4096
  38. 7
  39. 91
  40. 11

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