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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 673 · 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 36² and 37²?
  2. 2.A square garden has an area of 841 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 686 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 144 (b) 149 (c) 150
  6. 6.What is √961? =
  7. 7.Which of these is a perfect square? (a) 1156 (b) 1204 (c) 1190
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √1681? =
  10. 10.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  11. 11.What is 59²? =
  12. 12.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  13. 13.How many whole numbers lie between 48² and 49²?
  14. 14.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 2401 square m. How long is each side (in m)?
  16. 16.Which of these is a perfect square? (a) 690 (b) 676 (c) 699
  17. 17.What is 42²? =
  18. 18.What is 76²? =
  19. 19.A square garden has an area of 784 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 240 must be divided to get a perfect square?
  21. 21.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  22. 22.Which of these is a perfect square? (a) 625 (b) 628 (c) 662
  23. 23.A square garden has an area of 3249 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  26. 26.Which of these is a perfect square? (a) 1600 (b) 1673 (c) 1602
  27. 27.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  28. 28.What is √1369? =
  29. 29.Which of these is a perfect square? (a) 468 (b) 464 (c) 441
  30. 30.What is 72²? =
  31. 31.What is √441? =
  32. 32.What is √784? =
  33. 33.What is √1936? =
  34. 34.What is √3600? =
  35. 35.Which of these is a perfect square? (a) 196 (b) 223 (c) 213
  36. 36.What is the smallest whole number by which 150 must be divided to get a perfect square?
  37. 37.What is 84²? =
  38. 38.A square garden has an area of 400 square m. How long is each side (in m)?
  39. 39.What is 14²? =
  40. 40.A square garden has an area of 1764 square m. How long is each side (in m)?

Answer key

  1. 72
  2. 29
  3. 625
  4. 14
  5. 144
  6. 31
  7. 1156
  8. 36
  9. 41
  10. 10
  11. 3481
  12. 10
  13. 96
  14. 13
  15. 49
  16. 676
  17. 1764
  18. 5776
  19. 28
  20. 15
  21. 81
  22. 625
  23. 57
  24. 14
  25. 169
  26. 1600
  27. 14
  28. 37
  29. 441
  30. 5184
  31. 21
  32. 28
  33. 44
  34. 60
  35. 196
  36. 6
  37. 7056
  38. 20
  39. 196
  40. 42

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