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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 531 · 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.How many whole numbers lie between 17² and 18²?
  2. 2.Which of these is a perfect square? (a) 136 (b) 121 (c) 126
  3. 3.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  4. 4.A square garden has an area of 169 square m. How long is each side (in m)?
  5. 5.What is 75²? =
  6. 6.What is √4761? =
  7. 7.How many whole numbers lie between 5² and 6²?
  8. 8.How many whole numbers lie between 16² and 17²?
  9. 9.What is √4356? =
  10. 10.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  11. 11.What is √1600? =
  12. 12.A square garden has an area of 2601 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  14. 14.A square garden has an area of 1296 square m. How long is each side (in m)?
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √6724? =
  18. 18.A square garden has an area of 36 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  20. 20.How many whole numbers lie between 34² and 35²?
  21. 21.What is √6561? =
  22. 22.How many whole numbers lie between 32² and 33²?
  23. 23.Which of these is a perfect square? (a) 576 (b) 621 (c) 578
  24. 24.Which of these is a perfect square? (a) 970 (b) 1002 (c) 961
  25. 25.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 1521 square m. How long is each side (in m)?
  27. 27.A square garden has an area of 1764 square m. How long is each side (in m)?
  28. 28.What is 81²? =
  29. 29.What is √576? =
  30. 30.A square garden has an area of 625 square m. How long is each side (in m)?
  31. 31.Which of these is a perfect square? (a) 625 (b) 665 (c) 671
  32. 32.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 98²? =
  35. 35.How many whole numbers lie between 13² and 14²?
  36. 36.What is √9801? =
  37. 37.Which of these is a perfect square? (a) 455 (b) 441 (c) 475
  38. 38.Which of these is a perfect square? (a) 1296 (b) 1297 (c) 1327
  39. 39.What is √1024? =
  40. 40.A square garden has an area of 1369 square m. How long is each side (in m)?

Answer key

  1. 34
  2. 121
  3. 3
  4. 13
  5. 5625
  6. 69
  7. 10
  8. 32
  9. 66
  10. 2
  11. 40
  12. 51
  13. 900
  14. 36
  15. 576
  16. 784
  17. 82
  18. 6
  19. 7
  20. 68
  21. 81
  22. 64
  23. 576
  24. 961
  25. 676
  26. 39
  27. 42
  28. 6561
  29. 24
  30. 25
  31. 625
  32. 3
  33. 121
  34. 9604
  35. 26
  36. 99
  37. 441
  38. 1296
  39. 32
  40. 37

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