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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 347 · 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.Which of these is a perfect square? (a) 1225 (b) 1267 (c) 1240
  2. 2.What is √2601? =
  3. 3.What is 16²? =
  4. 4.What is 22²? =
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 17² and 18²?
  7. 7.Which of these is a perfect square? (a) 400 (b) 409 (c) 421
  8. 8.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  9. 9.What is √729? =
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √2304? =
  12. 12.What is 82²? =
  13. 13.What is 42²? =
  14. 14.What is √841? =
  15. 15.How many whole numbers lie between 44² and 45²?
  16. 16.What is the smallest whole number by which 126 must be divided to get a perfect square?
  17. 17.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  19. 19.How many whole numbers lie between 28² and 29²?
  20. 20.What is 18²? =
  21. 21.How many whole numbers lie between 14² and 15²?
  22. 22.A square garden has an area of 36 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 289 (b) 302 (c) 310
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 30² and 31²?
  26. 26.What is √576? =
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 2116 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 46² and 47²?
  30. 30.What is 87²? =
  31. 31.What is √5184? =
  32. 32.What is √1369? =
  33. 33.A square garden has an area of 256 square m. How long is each side (in m)?
  34. 34.What is 20²? =
  35. 35.What is √7569? =
  36. 36.Which of these is a perfect square? (a) 342 (b) 324 (c) 352
  37. 37.How many whole numbers lie between 45² and 46²?
  38. 38.Which of these is a perfect square? (a) 196 (b) 197 (c) 201
  39. 39.What is 12²? =
  40. 40.What is √9604? =

Answer key

  1. 1225
  2. 51
  3. 256
  4. 484
  5. 841
  6. 34
  7. 400
  8. 15
  9. 27
  10. 225
  11. 48
  12. 6724
  13. 1764
  14. 29
  15. 88
  16. 14
  17. 15
  18. 729
  19. 56
  20. 324
  21. 28
  22. 6
  23. 289
  24. 400
  25. 60
  26. 24
  27. 121
  28. 46
  29. 92
  30. 7569
  31. 72
  32. 37
  33. 16
  34. 400
  35. 87
  36. 324
  37. 90
  38. 196
  39. 144
  40. 98

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