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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 167 · 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 √225? =
  2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 20² and 21²?
  4. 4.Which of these is a perfect square? (a) 1296 (b) 1311 (c) 1333
  5. 5.What is √7569? =
  6. 6.How many whole numbers lie between 15² and 16²?
  7. 7.What is √2809? =
  8. 8.What is √7921? =
  9. 9.Which of these is a perfect square? (a) 214 (b) 216 (c) 196
  10. 10.Which of these is a perfect square? (a) 826 (b) 801 (c) 784
  11. 11.What is the smallest whole number by which 147 must be divided to get a perfect square?
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 48²? =
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  16. 16.A square garden has an area of 2601 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 50² and 51²?
  19. 19.What is √169? =
  20. 20.Which of these is a perfect square? (a) 414 (b) 420 (c) 400
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 14² and 15²?
  23. 23.Which of these is a perfect square? (a) 121 (b) 135 (c) 126
  24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 358 (b) 355 (c) 324
  26. 26.A square garden has an area of 400 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 5² and 6²?
  28. 28.A square garden has an area of 1936 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 289 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 1369 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 22²? =
  33. 33.A square garden has an area of 1600 square m. How long is each side (in m)?
  34. 34.What is 95²? =
  35. 35.How many whole numbers lie between 44² and 45²?
  36. 36.How many whole numbers lie between 27² and 28²?
  37. 37.What is the smallest whole number by which 294 must be divided to get a perfect square?
  38. 38.Which of these is a perfect square? (a) 374 (b) 389 (c) 361
  39. 39.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  40. 40.What is 20²? =

Answer key

  1. 15
  2. 576
  3. 40
  4. 1296
  5. 87
  6. 30
  7. 53
  8. 89
  9. 196
  10. 784
  11. 3
  12. 169
  13. 81
  14. 2304
  15. 100
  16. 51
  17. 144
  18. 100
  19. 13
  20. 400
  21. 64
  22. 28
  23. 121
  24. 729
  25. 324
  26. 20
  27. 10
  28. 44
  29. 17
  30. 37
  31. 289
  32. 484
  33. 40
  34. 9025
  35. 88
  36. 54
  37. 6
  38. 361
  39. 10
  40. 400

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