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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 565 · 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 79²? =
  2. 2.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  3. 3.What is 93²? =
  4. 4.What is 98²? =
  5. 5.A square garden has an area of 2304 square m. How long is each side (in m)?
  6. 6.What is √2025? =
  7. 7.What is √324? =
  8. 8.What is 87²? =
  9. 9.What is the smallest whole number by which 686 must be divided to get a perfect square?
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  11. 11.Which of these is a perfect square? (a) 789 (b) 803 (c) 784
  12. 12.What is √9025? =
  13. 13.What is 47²? =
  14. 14.Which of these is a perfect square? (a) 599 (b) 576 (c) 591
  15. 15.A square garden has an area of 1156 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 1681 square m. How long is each side (in m)?
  17. 17.What is the smallest whole number by which 176 must be divided to get a perfect square?
  18. 18.How many whole numbers lie between 19² and 20²?
  19. 19.A square garden has an area of 81 square m. How long is each side (in m)?
  20. 20.What is 42²? =
  21. 21.How many whole numbers lie between 35² and 36²?
  22. 22.How many whole numbers lie between 32² and 33²?
  23. 23.What is √1225? =
  24. 24.What is the smallest whole number by which 960 must be divided to get a perfect square?
  25. 25.What is √400? =
  26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1444 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 50²? =
  30. 30.What is the smallest whole number by which 126 must be divided to get a perfect square?
  31. 31.What is 83²? =
  32. 32.What is the smallest whole number by which 891 must be divided to get a perfect square?
  33. 33.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 1849 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 291 (b) 303 (c) 289
  36. 36.What is 23²? =
  37. 37.What is √7744? =
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 26²? =
  40. 40.Which of these is a perfect square? (a) 234 (b) 228 (c) 225

Answer key

  1. 6241
  2. 11
  3. 8649
  4. 9604
  5. 48
  6. 45
  7. 18
  8. 7569
  9. 14
  10. 100
  11. 784
  12. 95
  13. 2209
  14. 576
  15. 34
  16. 41
  17. 11
  18. 38
  19. 9
  20. 1764
  21. 70
  22. 64
  23. 35
  24. 15
  25. 20
  26. 25
  27. 38
  28. 441
  29. 2500
  30. 14
  31. 6889
  32. 11
  33. 676
  34. 43
  35. 289
  36. 529
  37. 88
  38. 64
  39. 676
  40. 225

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