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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 105 · 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.How many whole numbers lie between 18² and 19²?
  2. 2.How many whole numbers lie between 31² and 32²?
  3. 3.Which of these is a perfect square? (a) 1521 (b) 1585 (c) 1537
  4. 4.What is √576? =
  5. 5.Which of these is a perfect square? (a) 690 (b) 709 (c) 676
  6. 6.A square garden has an area of 1225 square m. How long is each side (in m)?
  7. 7.What is √1444? =
  8. 8.What is √1521? =
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 289 (b) 302 (c) 290
  12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 16² and 17²?
  15. 15.How many whole numbers lie between 32² and 33²?
  16. 16.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1415 (b) 1369 (c) 1413
  18. 18.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  19. 19.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  21. 21.How many whole numbers lie between 14² and 15²?
  22. 22.What is 11²? =
  23. 23.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 784 square m. How long is each side (in m)?
  25. 25.What is √1764? =
  26. 26.What is 20²? =
  27. 27.What is 26²? =
  28. 28.How many whole numbers lie between 26² and 27²?
  29. 29.A square garden has an area of 676 square m. How long is each side (in m)?
  30. 30.What is √2209? =
  31. 31.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  32. 32.What is 91²? =
  33. 33.Which of these is a perfect square? (a) 667 (b) 625 (c) 634
  34. 34.A square garden has an area of 1156 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 1226 (b) 1225 (c) 1250
  36. 36.What is 54²? =
  37. 37.What is 69²? =
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  40. 40.What is 36²? =

Answer key

  1. 36
  2. 62
  3. 1521
  4. 24
  5. 676
  6. 35
  7. 38
  8. 39
  9. 25
  10. 7
  11. 289
  12. 484
  13. 361
  14. 32
  15. 64
  16. 13
  17. 1369
  18. 10
  19. 324
  20. 81
  21. 28
  22. 121
  23. 3
  24. 28
  25. 42
  26. 400
  27. 676
  28. 52
  29. 26
  30. 47
  31. 5
  32. 8281
  33. 625
  34. 34
  35. 1225
  36. 2916
  37. 4761
  38. 54
  39. 5
  40. 1296

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