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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 421 · 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 25 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 27² and 28²?
  4. 4.What is 81²? =
  5. 5.What is √8464? =
  6. 6.What is the smallest whole number by which 252 must be divided to get a perfect square?
  7. 7.What is √1369? =
  8. 8.What is 14²? =
  9. 9.What is 63²? =
  10. 10.Which of these is a perfect square? (a) 207 (b) 208 (c) 196
  11. 11.A square garden has an area of 225 square m. How long is each side (in m)?
  12. 12.What is √1764? =
  13. 13.What is 97²? =
  14. 14.What is 48²? =
  15. 15.What is the smallest whole number by which 90 must be divided to get a perfect square?
  16. 16.Which of these is a perfect square? (a) 746 (b) 735 (c) 729
  17. 17.A square garden has an area of 1444 square m. How long is each side (in m)?
  18. 18.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 576 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 961 (b) 1009 (c) 1008
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √7921? =
  25. 25.What is 24²? =
  26. 26.What is 19²? =
  27. 27.A square garden has an area of 81 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  29. 29.A square garden has an area of 3364 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 14² and 15²?
  31. 31.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 288 (b) 281 (c) 256
  33. 33.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 76²? =
  35. 35.A square garden has an area of 841 square m. How long is each side (in m)?
  36. 36.What is 64²? =
  37. 37.What is √2304? =
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 16² and 17²?
  40. 40.What is √1521? =

Answer key

  1. 625
  2. 2
  3. 54
  4. 6561
  5. 92
  6. 7
  7. 37
  8. 196
  9. 3969
  10. 196
  11. 15
  12. 42
  13. 9409
  14. 2304
  15. 10
  16. 729
  17. 38
  18. 2
  19. 484
  20. 24
  21. 17
  22. 961
  23. 25
  24. 89
  25. 576
  26. 361
  27. 9
  28. 14
  29. 58
  30. 28
  31. 15
  32. 256
  33. 576
  34. 5776
  35. 29
  36. 4096
  37. 48
  38. 441
  39. 32
  40. 39

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