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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 321 · 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 the smallest whole number by which 18 must be divided to get a perfect square?
  2. 2.Which of these is a perfect square? (a) 103 (b) 115 (c) 100
  3. 3.A square garden has an area of 1521 square m. How long is each side (in m)?
  4. 4.A square garden has an area of 784 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  6. 6.What is √3481? =
  7. 7.What is 21²? =
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 58²? =
  10. 10.A square garden has an area of 1764 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  12. 12.What is 12²? =
  13. 13.A square garden has an area of 1156 square m. How long is each side (in m)?
  14. 14.What is √225? =
  15. 15.What is the smallest whole number by which 810 must be divided to get a perfect square?
  16. 16.What is 29²? =
  17. 17.Which of these is a perfect square? (a) 445 (b) 478 (c) 441
  18. 18.Which of these is a perfect square? (a) 1448 (b) 1444 (c) 1494
  19. 19.What is the smallest whole number by which 20 must be divided to get a perfect square?
  20. 20.What is √7569? =
  21. 21.What is √361? =
  22. 22.Which of these is a perfect square? (a) 1420 (b) 1411 (c) 1369
  23. 23.A square garden has an area of 441 square m. How long is each side (in m)?
  24. 24.What is 24²? =
  25. 25.A square garden has an area of 2704 square m. How long is each side (in m)?
  26. 26.A square garden has an area of 25 square m. How long is each side (in m)?
  27. 27.What is √576? =
  28. 28.What is √7225? =
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is 95²? =
  31. 31.How many whole numbers lie between 37² and 38²?
  32. 32.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  33. 33.What is √1156? =
  34. 34.What is 64²? =
  35. 35.How many whole numbers lie between 13² and 14²?
  36. 36.What is √121? =
  37. 37.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  38. 38.What is 71²? =
  39. 39.What is 31²? =
  40. 40.What is √5929? =

Answer key

  1. 2
  2. 100
  3. 39
  4. 28
  5. 11
  6. 59
  7. 441
  8. 324
  9. 3364
  10. 42
  11. 7
  12. 144
  13. 34
  14. 15
  15. 10
  16. 841
  17. 441
  18. 1444
  19. 5
  20. 87
  21. 19
  22. 1369
  23. 21
  24. 576
  25. 52
  26. 5
  27. 24
  28. 85
  29. 100
  30. 9025
  31. 74
  32. 5
  33. 34
  34. 4096
  35. 26
  36. 11
  37. 3
  38. 5041
  39. 961
  40. 77

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