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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 69 · 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 √2025? =
  2. 2.What is the smallest whole number by which 486 must be divided to get a perfect square?
  3. 3.How many whole numbers lie between 10² and 11²?
  4. 4.A square garden has an area of 2304 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 1225 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  8. 8.What is 54²? =
  9. 9.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 319 (b) 289 (c) 323
  12. 12.Which of these is a perfect square? (a) 1534 (b) 1521 (c) 1568
  13. 13.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  14. 14.A square garden has an area of 1444 square m. How long is each side (in m)?
  15. 15.What is 34²? =
  16. 16.What is 13²? =
  17. 17.What is 17²? =
  18. 18.How many whole numbers lie between 41² and 42²?
  19. 19.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  20. 20.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  21. 21.What is 82²? =
  22. 22.What is 56²? =
  23. 23.What is √1296? =
  24. 24.What is √5625? =
  25. 25.How many whole numbers lie between 6² and 7²?
  26. 26.What is 22²? =
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 17² and 18²?
  30. 30.A square garden has an area of 2209 square m. How long is each side (in m)?
  31. 31.What is √361? =
  32. 32.How many whole numbers lie between 7² and 8²?
  33. 33.How many whole numbers lie between 21² and 22²?
  34. 34.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
  35. 35.What is √1600? =
  36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  37. 37.How many whole numbers lie between 15² and 16²?
  38. 38.Which of these is a perfect square? (a) 1296 (b) 1344 (c) 1309
  39. 39.What is √1444? =
  40. 40.How many whole numbers lie between 11² and 12²?

Answer key

  1. 45
  2. 6
  3. 20
  4. 48
  5. 5
  6. 35
  7. 14
  8. 2916
  9. 81
  10. 15
  11. 289
  12. 1521
  13. 13
  14. 38
  15. 1156
  16. 169
  17. 289
  18. 82
  19. 15
  20. 11
  21. 6724
  22. 3136
  23. 36
  24. 75
  25. 12
  26. 484
  27. 484
  28. 64
  29. 34
  30. 47
  31. 19
  32. 14
  33. 42
  34. 6
  35. 40
  36. 676
  37. 30
  38. 1296
  39. 38
  40. 22

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