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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 295 · 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 75 must be divided to get a perfect square?
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 20² and 21²?
  5. 5.What is the smallest whole number by which 18 must be divided to get a perfect square?
  6. 6.What is 39²? =
  7. 7.A square garden has an area of 3481 square m. How long is each side (in m)?
  8. 8.How many whole numbers lie between 28² and 29²?
  9. 9.What is the smallest whole number by which 56 must be divided to get a perfect square?
  10. 10.What is 72²? =
  11. 11.What is √289? =
  12. 12.How many whole numbers lie between 7² and 8²?
  13. 13.A square garden has an area of 2025 square m. How long is each side (in m)?
  14. 14.Which of these is a perfect square? (a) 196 (b) 217 (c) 198
  15. 15.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
  16. 16.What is 42²? =
  17. 17.What is the smallest whole number by which 375 must be divided to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 1002 (b) 981 (c) 961
  19. 19.Which of these is a perfect square? (a) 256 (b) 288 (c) 258
  20. 20.What is √3600? =
  21. 21.Which of these is a perfect square? (a) 330 (b) 355 (c) 324
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  23. 23.Which of these is a perfect square? (a) 955 (b) 947 (c) 900
  24. 24.Which of these is a perfect square? (a) 1600 (b) 1667 (c) 1629
  25. 25.A square garden has an area of 64 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 12² and 13²?
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √2304? =
  29. 29.What is 21²? =
  30. 30.Which of these is a perfect square? (a) 734 (b) 729 (c) 764
  31. 31.Which of these is a perfect square? (a) 141 (b) 139 (c) 121
  32. 32.How many whole numbers lie between 13² and 14²?
  33. 33.How many whole numbers lie between 46² and 47²?
  34. 34.What is √196? =
  35. 35.A square garden has an area of 169 square m. How long is each side (in m)?
  36. 36.What is √784? =
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 890 (b) 862 (c) 841
  39. 39.What is the smallest whole number by which 28 must be divided to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 100 (b) 120 (c) 102

Answer key

  1. 3
  2. 256
  3. 36
  4. 40
  5. 2
  6. 1521
  7. 59
  8. 56
  9. 14
  10. 5184
  11. 17
  12. 14
  13. 45
  14. 196
  15. 10
  16. 1764
  17. 15
  18. 961
  19. 256
  20. 60
  21. 324
  22. 144
  23. 900
  24. 1600
  25. 8
  26. 24
  27. 900
  28. 48
  29. 441
  30. 729
  31. 121
  32. 26
  33. 92
  34. 14
  35. 13
  36. 28
  37. 361
  38. 841
  39. 7
  40. 100

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