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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 20 · 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.A square garden has an area of 1369 square m. How long is each side (in m)?
  2. 2.A square garden has an area of 2500 square m. How long is each side (in m)?
  3. 3.What is √529? =
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 343 (b) 324 (c) 356
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  7. 7.A square garden has an area of 225 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 1090 (b) 1110 (c) 1089
  9. 9.What is 48²? =
  10. 10.How many whole numbers lie between 22² and 23²?
  11. 11.How many whole numbers lie between 9² and 10²?
  12. 12.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 225 (b) 234 (c) 238
  14. 14.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 121 (b) 128 (c) 137
  16. 16.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  17. 17.What is √3481? =
  18. 18.How many whole numbers lie between 31² and 32²?
  19. 19.What is 53²? =
  20. 20.What is the smallest whole number by which 147 must be divided to get a perfect square?
  21. 21.A square garden has an area of 81 square m. How long is each side (in m)?
  22. 22.What is √1521? =
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 1296 square m. How long is each side (in m)?
  25. 25.What is 61²? =
  26. 26.Which of these is a perfect square? (a) 157 (b) 144 (c) 155
  27. 27.What is 25²? =
  28. 28.Which of these is a perfect square? (a) 1570 (b) 1581 (c) 1521
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 46² and 47²?
  31. 31.How many whole numbers lie between 25² and 26²?
  32. 32.A square garden has an area of 2304 square m. How long is each side (in m)?
  33. 33.Which of these is a perfect square? (a) 452 (b) 469 (c) 441
  34. 34.What is the smallest whole number by which 252 must be divided to get a perfect square?
  35. 35.What is 76²? =
  36. 36.What is the smallest whole number by which 72 must be divided to get a perfect square?
  37. 37.What is the smallest whole number by which 896 must be divided to get a perfect square?
  38. 38.What is √625? =
  39. 39.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 48 must be multiplied to get a perfect square?

Answer key

  1. 37
  2. 50
  3. 23
  4. 576
  5. 324
  6. 169
  7. 15
  8. 1089
  9. 2304
  10. 44
  11. 18
  12. 7
  13. 225
  14. 14
  15. 121
  16. 15
  17. 59
  18. 62
  19. 2809
  20. 3
  21. 9
  22. 39
  23. 121
  24. 36
  25. 3721
  26. 144
  27. 625
  28. 1521
  29. 289
  30. 92
  31. 50
  32. 48
  33. 441
  34. 7
  35. 5776
  36. 2
  37. 14
  38. 25
  39. 14
  40. 3

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