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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 308 · 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) 256 (b) 259 (c) 284
  2. 2.A square garden has an area of 441 square m. How long is each side (in m)?
  3. 3.What is 90²? =
  4. 4.What is 36²? =
  5. 5.How many whole numbers lie between 43² and 44²?
  6. 6.A square garden has an area of 625 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 1674 (b) 1624 (c) 1600
  8. 8.How many whole numbers lie between 39² and 40²?
  9. 9.What is the smallest whole number by which 350 must be divided to get a perfect square?
  10. 10.How many whole numbers lie between 14² and 15²?
  11. 11.Which of these is a perfect square? (a) 625 (b) 649 (c) 638
  12. 12.How many whole numbers lie between 32² and 33²?
  13. 13.Which of these is a perfect square? (a) 157 (b) 145 (c) 144
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √2500? =
  16. 16.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 81 square m. How long is each side (in m)?
  18. 18.What is 74²? =
  19. 19.Which of these is a perfect square? (a) 680 (b) 683 (c) 676
  20. 20.How many whole numbers lie between 45² and 46²?
  21. 21.How many whole numbers lie between 8² and 9²?
  22. 22.What is √5625? =
  23. 23.Which of these is a perfect square? (a) 837 (b) 806 (c) 784
  24. 24.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  25. 25.What is the smallest whole number by which 12 must be divided to get a perfect square?
  26. 26.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  27. 27.What is √3249? =
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √1444? =
  30. 30.How many whole numbers lie between 27² and 28²?
  31. 31.What is √400? =
  32. 32.What is the smallest whole number by which 32 must be divided to get a perfect square?
  33. 33.A square garden has an area of 1369 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is √5184? =
  36. 36.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 1296 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 1092 (b) 1089 (c) 1100
  39. 39.Which of these is a perfect square? (a) 1225 (b) 1233 (c) 1226
  40. 40.How many whole numbers lie between 13² and 14²?

Answer key

  1. 256
  2. 21
  3. 8100
  4. 1296
  5. 86
  6. 25
  7. 1600
  8. 78
  9. 14
  10. 28
  11. 625
  12. 64
  13. 144
  14. 64
  15. 50
  16. 529
  17. 9
  18. 5476
  19. 676
  20. 90
  21. 16
  22. 75
  23. 784
  24. 10
  25. 3
  26. 14
  27. 57
  28. 841
  29. 38
  30. 54
  31. 20
  32. 2
  33. 37
  34. 121
  35. 72
  36. 5
  37. 36
  38. 1089
  39. 1225
  40. 26

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