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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 455 · 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) 167 (b) 166 (c) 144
  2. 2.Which of these is a perfect square? (a) 1166 (b) 1156 (c) 1220
  3. 3.A square garden has an area of 2500 square m. How long is each side (in m)?
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  6. 6.Which of these is a perfect square? (a) 916 (b) 930 (c) 900
  7. 7.Which of these is a perfect square? (a) 131 (b) 138 (c) 121
  8. 8.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  9. 9.Which of these is a perfect square? (a) 187 (b) 174 (c) 169
  10. 10.A square garden has an area of 1024 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 6² and 7²?
  12. 12.How many whole numbers lie between 45² and 46²?
  13. 13.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  14. 14.What is √7744? =
  15. 15.What is √2601? =
  16. 16.How many whole numbers lie between 25² and 26²?
  17. 17.What is the smallest whole number by which 208 must be divided to get a perfect square?
  18. 18.A square garden has an area of 256 square m. How long is each side (in m)?
  19. 19.What is √7921? =
  20. 20.What is √289? =
  21. 21.What is √3249? =
  22. 22.What is 14²? =
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is √6889? =
  25. 25.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  26. 26.What is 48²? =
  27. 27.How many whole numbers lie between 42² and 43²?
  28. 28.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 384 (b) 361 (c) 366
  30. 30.Which of these is a perfect square? (a) 762 (b) 729 (c) 746
  31. 31.A square garden has an area of 841 square m. How long is each side (in m)?
  32. 32.What is 13²? =
  33. 33.What is √625? =
  34. 34.What is √1681? =
  35. 35.Which of these is a perfect square? (a) 432 (b) 420 (c) 400
  36. 36.Which of these is a perfect square? (a) 1369 (b) 1436 (c) 1377
  37. 37.What is 45²? =
  38. 38.A square garden has an area of 484 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 2025 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 40 must be divided to get a perfect square?

Answer key

  1. 144
  2. 1156
  3. 50
  4. 25
  5. 15
  6. 900
  7. 121
  8. 10
  9. 169
  10. 32
  11. 12
  12. 90
  13. 10
  14. 88
  15. 51
  16. 50
  17. 13
  18. 16
  19. 89
  20. 17
  21. 57
  22. 196
  23. 576
  24. 83
  25. 10
  26. 2304
  27. 84
  28. 5
  29. 361
  30. 729
  31. 29
  32. 169
  33. 25
  34. 41
  35. 400
  36. 1369
  37. 2025
  38. 22
  39. 45
  40. 10

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