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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 281 · 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.Which of these is a perfect square? (a) 183 (b) 169 (c) 175
  2. 2.What is 78²? =
  3. 3.How many whole numbers lie between 35² and 36²?
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 320 must be divided to get a perfect square?
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 324 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 1600 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 12 must be divided to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 512 (b) 499 (c) 484
  11. 11.What is the smallest whole number by which 243 must be divided to get a perfect square?
  12. 12.How many whole numbers lie between 43² and 44²?
  13. 13.What is 92²? =
  14. 14.How many whole numbers lie between 46² and 47²?
  15. 15.What is 39²? =
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 126 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  19. 19.What is 70²? =
  20. 20.What is √2025? =
  21. 21.How many whole numbers lie between 13² and 14²?
  22. 22.What is √4624? =
  23. 23.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 2209 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 960 must be divided to get a perfect square?
  26. 26.A square garden has an area of 729 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 3364 square m. How long is each side (in m)?
  28. 28.What is the smallest whole number by which 245 must be divided to get a perfect square?
  29. 29.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  30. 30.What is 90²? =
  31. 31.What is √1369? =
  32. 32.What is √529? =
  33. 33.What is 24²? =
  34. 34.A square garden has an area of 1764 square m. How long is each side (in m)?
  35. 35.What is √3364? =
  36. 36.How many whole numbers lie between 19² and 20²?
  37. 37.What is 47²? =
  38. 38.How many whole numbers lie between 39² and 40²?
  39. 39.What is √1444? =
  40. 40.A square garden has an area of 1849 square m. How long is each side (in m)?

Answer key

  1. 169
  2. 6084
  3. 70
  4. 225
  5. 5
  6. 36
  7. 18
  8. 40
  9. 3
  10. 484
  11. 3
  12. 86
  13. 8464
  14. 92
  15. 1521
  16. 121
  17. 14
  18. 15
  19. 4900
  20. 45
  21. 26
  22. 68
  23. 7
  24. 47
  25. 15
  26. 27
  27. 58
  28. 5
  29. 3
  30. 8100
  31. 37
  32. 23
  33. 576
  34. 42
  35. 58
  36. 38
  37. 2209
  38. 78
  39. 38
  40. 43

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