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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 584 · 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.How many whole numbers lie between 12² and 13²?
  2. 2.What is 51²? =
  3. 3.What is √7396? =
  4. 4.What is 84²? =
  5. 5.A square garden has an area of 49 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 196 square m. How long is each side (in m)?
  8. 8.What is √784? =
  9. 9.A square garden has an area of 2304 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 14² and 15²?
  11. 11.Which of these is a perfect square? (a) 184 (b) 170 (c) 169
  12. 12.A square garden has an area of 784 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 77²? =
  15. 15.How many whole numbers lie between 35² and 36²?
  16. 16.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1507 (b) 1467 (c) 1444
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1296 (b) 1299 (c) 1354
  20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 60 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 13² and 14²?
  24. 24.How many whole numbers lie between 8² and 9²?
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 112 (b) 100 (c) 106
  27. 27.What is the smallest whole number by which 375 must be divided to get a perfect square?
  28. 28.What is 61²? =
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is 28²? =
  32. 32.A square garden has an area of 1089 square m. How long is each side (in m)?
  33. 33.What is √3025? =
  34. 34.A square garden has an area of 64 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 3600 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 2809 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 2601 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 388 (b) 363 (c) 361
  40. 40.A square garden has an area of 3364 square m. How long is each side (in m)?

Answer key

  1. 24
  2. 2601
  3. 86
  4. 7056
  5. 7
  6. 169
  7. 14
  8. 28
  9. 48
  10. 28
  11. 169
  12. 28
  13. 81
  14. 5929
  15. 70
  16. 5
  17. 1444
  18. 361
  19. 1296
  20. 64
  21. 144
  22. 15
  23. 26
  24. 16
  25. 400
  26. 100
  27. 15
  28. 3721
  29. 121
  30. 25
  31. 784
  32. 33
  33. 55
  34. 8
  35. 60
  36. 729
  37. 53
  38. 51
  39. 361
  40. 58

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