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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 272 · 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.A square garden has an area of 1936 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 804 (b) 807 (c) 784
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 1089 square m. How long is each side (in m)?
  6. 6.What is √2401? =
  7. 7.Which of these is a perfect square? (a) 1521 (b) 1554 (c) 1526
  8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 46²? =
  10. 10.How many whole numbers lie between 17² and 18²?
  11. 11.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 6² and 7²?
  13. 13.What is √121? =
  14. 14.What is √7396? =
  15. 15.What is √6241? =
  16. 16.What is √961? =
  17. 17.How many whole numbers lie between 38² and 39²?
  18. 18.What is √3969? =
  19. 19.How many whole numbers lie between 10² and 11²?
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √5625? =
  22. 22.Which of these is a perfect square? (a) 593 (b) 602 (c) 576
  23. 23.How many whole numbers lie between 37² and 38²?
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 169 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 173 (b) 169 (c) 183
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 256 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 162 must be divided to get a perfect square?
  31. 31.What is √1369? =
  32. 32.What is √4761? =
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 77²? =
  35. 35.Which of these is a perfect square? (a) 100 (b) 116 (c) 107
  36. 36.What is 97²? =
  37. 37.What is the smallest whole number by which 63 must be divided to get a perfect square?
  38. 38.A square garden has an area of 2704 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 960 must be divided to get a perfect square?
  40. 40.What is 19²? =

Answer key

  1. 44
  2. 900
  3. 784
  4. 484
  5. 33
  6. 49
  7. 1521
  8. 64
  9. 2116
  10. 34
  11. 5
  12. 12
  13. 11
  14. 86
  15. 79
  16. 31
  17. 76
  18. 63
  19. 20
  20. 144
  21. 75
  22. 576
  23. 74
  24. 529
  25. 13
  26. 169
  27. 100
  28. 676
  29. 16
  30. 2
  31. 37
  32. 69
  33. 49
  34. 5929
  35. 100
  36. 9409
  37. 7
  38. 52
  39. 15
  40. 361

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