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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 250 · 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 46²? =
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 11² and 12²?
  6. 6.What is √4489? =
  7. 7.A square garden has an area of 361 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  9. 9.What is √5625? =
  10. 10.Which of these is a perfect square? (a) 961 (b) 992 (c) 993
  11. 11.How many whole numbers lie between 27² and 28²?
  12. 12.Which of these is a perfect square? (a) 126 (b) 121 (c) 140
  13. 13.A square garden has an area of 1296 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 196 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 3025 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 245 must be divided to get a perfect square?
  17. 17.What is √9409? =
  18. 18.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 1600 (b) 1623 (c) 1607
  20. 20.What is √5329? =
  21. 21.How many whole numbers lie between 13² and 14²?
  22. 22.A square garden has an area of 225 square m. How long is each side (in m)?
  23. 23.What is √1444? =
  24. 24.How many whole numbers lie between 24² and 25²?
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 47² and 48²?
  28. 28.Which of these is a perfect square? (a) 714 (b) 702 (c) 676
  29. 29.A square garden has an area of 25 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 288 (b) 256 (c) 265
  31. 31.What is √3025? =
  32. 32.How many whole numbers lie between 26² and 27²?
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 206 (b) 196 (c) 215
  36. 36.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  37. 37.A square garden has an area of 1225 square m. How long is each side (in m)?
  38. 38.Which of these is a perfect square? (a) 663 (b) 625 (c) 634
  39. 39.A square garden has an area of 3364 square m. How long is each side (in m)?
  40. 40.What is 48²? =

Answer key

  1. 2116
  2. 100
  3. 6
  4. 225
  5. 22
  6. 67
  7. 19
  8. 13
  9. 75
  10. 961
  11. 54
  12. 121
  13. 36
  14. 14
  15. 55
  16. 5
  17. 97
  18. 196
  19. 1600
  20. 73
  21. 26
  22. 15
  23. 38
  24. 48
  25. 256
  26. 324
  27. 94
  28. 676
  29. 5
  30. 256
  31. 55
  32. 52
  33. 64
  34. 11
  35. 196
  36. 15
  37. 35
  38. 625
  39. 58
  40. 2304

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