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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 320 · 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 15 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 28² and 29²?
  3. 3.What is √1296? =
  4. 4.A square garden has an area of 3364 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 1089 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 349 (b) 331 (c) 324
  7. 7.What is the smallest whole number by which 32 must be divided to get a perfect square?
  8. 8.What is 52²? =
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 3249 square m. How long is each side (in m)?
  11. 11.What is √1764? =
  12. 12.A square garden has an area of 225 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 20² and 21²?
  14. 14.What is 20²? =
  15. 15.What is the smallest whole number by which 240 must be divided to get a perfect square?
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 1521 square m. How long is each side (in m)?
  18. 18.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  19. 19.What is √2500? =
  20. 20.A square garden has an area of 64 square m. How long is each side (in m)?
  21. 21.What is 66²? =
  22. 22.How many whole numbers lie between 30² and 31²?
  23. 23.How many whole numbers lie between 29² and 30²?
  24. 24.Which of these is a perfect square? (a) 195 (b) 169 (c) 180
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 690 (b) 676 (c) 720
  27. 27.A square garden has an area of 529 square m. How long is each side (in m)?
  28. 28.What is 42²? =
  29. 29.A square garden has an area of 3136 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 289 (b) 322 (c) 297
  31. 31.Which of these is a perfect square? (a) 991 (b) 961 (c) 964
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  33. 33.What is 48²? =
  34. 34.What is √4489? =
  35. 35.What is 69²? =
  36. 36.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  38. 38.What is the smallest whole number by which 320 must be divided to get a perfect square?
  39. 39.What is √256? =
  40. 40.How many whole numbers lie between 11² and 12²?

Answer key

  1. 225
  2. 56
  3. 36
  4. 58
  5. 33
  6. 324
  7. 2
  8. 2704
  9. 121
  10. 57
  11. 42
  12. 15
  13. 40
  14. 400
  15. 15
  16. 484
  17. 39
  18. 5
  19. 50
  20. 8
  21. 4356
  22. 60
  23. 58
  24. 169
  25. 441
  26. 676
  27. 23
  28. 1764
  29. 56
  30. 289
  31. 961
  32. 169
  33. 2304
  34. 67
  35. 4761
  36. 36
  37. 15
  38. 5
  39. 16
  40. 22

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