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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 494 · 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) 361 (b) 394 (c) 363
  2. 2.What is √529? =
  3. 3.What is 88²? =
  4. 4.How many whole numbers lie between 8² and 9²?
  5. 5.How many whole numbers lie between 15² and 16²?
  6. 6.A square garden has an area of 169 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 324 square m. How long is each side (in m)?
  8. 8.What is √961? =
  9. 9.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 1559 (b) 1523 (c) 1521
  11. 11.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  12. 12.What is √5776? =
  13. 13.What is √3721? =
  14. 14.What is √256? =
  15. 15.Which of these is a perfect square? (a) 169 (b) 177 (c) 186
  16. 16.A square garden has an area of 2209 square m. How long is each side (in m)?
  17. 17.What is √169? =
  18. 18.What is 67²? =
  19. 19.Which of these is a perfect square? (a) 153 (b) 168 (c) 144
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  21. 21.Which of these is a perfect square? (a) 1024 (b) 1027 (c) 1087
  22. 22.Which of these is a perfect square? (a) 976 (b) 961 (c) 989
  23. 23.A square garden has an area of 2601 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 144 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 1369 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 130 (b) 121 (c) 128
  28. 28.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  29. 29.What is √7744? =
  30. 30.How many whole numbers lie between 31² and 32²?
  31. 31.How many whole numbers lie between 5² and 6²?
  32. 32.What is √6241? =
  33. 33.Which of these is a perfect square? (a) 515 (b) 526 (c) 484
  34. 34.What is √6400? =
  35. 35.Which of these is a perfect square? (a) 576 (b) 603 (c) 577
  36. 36.What is 48²? =
  37. 37.Which of these is a perfect square? (a) 230 (b) 237 (c) 225
  38. 38.How many whole numbers lie between 30² and 31²?
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 12 must be divided to get a perfect square?

Answer key

  1. 361
  2. 23
  3. 7744
  4. 16
  5. 30
  6. 13
  7. 18
  8. 31
  9. 13
  10. 1521
  11. 14
  12. 76
  13. 61
  14. 16
  15. 169
  16. 47
  17. 13
  18. 4489
  19. 144
  20. 144
  21. 1024
  22. 961
  23. 51
  24. 12
  25. 37
  26. 784
  27. 121
  28. 15
  29. 88
  30. 62
  31. 10
  32. 79
  33. 484
  34. 80
  35. 576
  36. 2304
  37. 225
  38. 60
  39. 441
  40. 3

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