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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 276 · 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 √1225? =
  2. 2.What is 56²? =
  3. 3.Which of these is a perfect square? (a) 151 (b) 147 (c) 144
  4. 4.What is 22²? =
  5. 5.How many whole numbers lie between 14² and 15²?
  6. 6.What is the smallest whole number by which 896 must be divided to get a perfect square?
  7. 7.A square garden has an area of 100 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 117 must be divided to get a perfect square?
  9. 9.What is 55²? =
  10. 10.What is √8836? =
  11. 11.What is 15²? =
  12. 12.What is √2304? =
  13. 13.Which of these is a perfect square? (a) 273 (b) 279 (c) 256
  14. 14.What is the smallest whole number by which 108 must be divided to get a perfect square?
  15. 15.What is √3364? =
  16. 16.What is 20²? =
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 676 square m. How long is each side (in m)?
  19. 19.What is √6400? =
  20. 20.A square garden has an area of 2304 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 29² and 30²?
  22. 22.What is 99²? =
  23. 23.Which of these is a perfect square? (a) 1611 (b) 1630 (c) 1600
  24. 24.What is √400? =
  25. 25.What is 57²? =
  26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 441 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 44² and 45²?
  29. 29.A square garden has an area of 3136 square m. How long is each side (in m)?
  30. 30.What is √4225? =
  31. 31.How many whole numbers lie between 27² and 28²?
  32. 32.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 1849 square m. How long is each side (in m)?
  35. 35.What is √5476? =
  36. 36.What is √784? =
  37. 37.How many whole numbers lie between 40² and 41²?
  38. 38.How many whole numbers lie between 12² and 13²?
  39. 39.Which of these is a perfect square? (a) 361 (b) 393 (c) 392
  40. 40.What is 75²? =

Answer key

  1. 35
  2. 3136
  3. 144
  4. 484
  5. 28
  6. 14
  7. 10
  8. 13
  9. 3025
  10. 94
  11. 225
  12. 48
  13. 256
  14. 3
  15. 58
  16. 400
  17. 64
  18. 26
  19. 80
  20. 48
  21. 58
  22. 9801
  23. 1600
  24. 20
  25. 3249
  26. 676
  27. 21
  28. 88
  29. 56
  30. 65
  31. 54
  32. 289
  33. 144
  34. 43
  35. 74
  36. 28
  37. 80
  38. 24
  39. 361
  40. 5625

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