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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 279 · 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 2209 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 1521 (b) 1554 (c) 1530
  3. 3.How many whole numbers lie between 17² and 18²?
  4. 4.What is 26²? =
  5. 5.Which of these is a perfect square? (a) 684 (b) 725 (c) 676
  6. 6.What is √289? =
  7. 7.What is the smallest whole number by which 80 must be divided to get a perfect square?
  8. 8.What is √9801? =
  9. 9.What is the smallest whole number by which 44 must be divided to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 1617 (b) 1600 (c) 1618
  11. 11.How many whole numbers lie between 48² and 49²?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 8² and 9²?
  14. 14.Which of these is a perfect square? (a) 286 (b) 264 (c) 256
  15. 15.How many whole numbers lie between 28² and 29²?
  16. 16.Which of these is a perfect square? (a) 729 (b) 736 (c) 748
  17. 17.What is 37²? =
  18. 18.How many whole numbers lie between 25² and 26²?
  19. 19.Which of these is a perfect square? (a) 141 (b) 123 (c) 121
  20. 20.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  21. 21.How many whole numbers lie between 39² and 40²?
  22. 22.What is 71²? =
  23. 23.What is 14²? =
  24. 24.Which of these is a perfect square? (a) 1311 (b) 1296 (c) 1323
  25. 25.A square garden has an area of 2601 square m. How long is each side (in m)?
  26. 26.What is 13²? =
  27. 27.A square garden has an area of 100 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 35² and 36²?
  29. 29.What is the smallest whole number by which 135 must be divided to get a perfect square?
  30. 30.Which of these is a perfect square? (a) 166 (b) 158 (c) 144
  31. 31.What is √5625? =
  32. 32.What is the smallest whole number by which 192 must be divided to get a perfect square?
  33. 33.What is 54²? =
  34. 34.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 624 (b) 590 (c) 576
  36. 36.What is 72²? =
  37. 37.What is the smallest whole number by which 63 must be divided to get a perfect square?
  38. 38.How many whole numbers lie between 40² and 41²?
  39. 39.What is √625? =
  40. 40.What is the smallest whole number by which 375 must be multiplied to get a perfect square?

Answer key

  1. 47
  2. 1521
  3. 34
  4. 676
  5. 676
  6. 17
  7. 5
  8. 99
  9. 11
  10. 1600
  11. 96
  12. 729
  13. 16
  14. 256
  15. 56
  16. 729
  17. 1369
  18. 50
  19. 121
  20. 11
  21. 78
  22. 5041
  23. 196
  24. 1296
  25. 51
  26. 169
  27. 10
  28. 70
  29. 15
  30. 144
  31. 75
  32. 3
  33. 2916
  34. 3
  35. 576
  36. 5184
  37. 7
  38. 80
  39. 25
  40. 15

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