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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 52 · 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 144 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  3. 3.Which of these is a perfect square? (a) 647 (b) 658 (c) 625
  4. 4.What is 77²? =
  5. 5.Which of these is a perfect square? (a) 386 (b) 388 (c) 361
  6. 6.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  7. 7.What is √1369? =
  8. 8.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  10. 10.What is √2116? =
  11. 11.How many whole numbers lie between 38² and 39²?
  12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  13. 13.A square garden has an area of 324 square m. How long is each side (in m)?
  14. 14.What is 60²? =
  15. 15.How many whole numbers lie between 5² and 6²?
  16. 16.What is 69²? =
  17. 17.What is √529? =
  18. 18.What is √841? =
  19. 19.What is 76²? =
  20. 20.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  21. 21.What is 24²? =
  22. 22.A square garden has an area of 2025 square m. How long is each side (in m)?
  23. 23.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  24. 24.What is 26²? =
  25. 25.How many whole numbers lie between 17² and 18²?
  26. 26.Which of these is a perfect square? (a) 1008 (b) 961 (c) 1001
  27. 27.Which of these is a perfect square? (a) 115 (b) 116 (c) 100
  28. 28.Which of these is a perfect square? (a) 1168 (b) 1196 (c) 1156
  29. 29.What is 85²? =
  30. 30.Which of these is a perfect square? (a) 527 (b) 500 (c) 484
  31. 31.A square garden has an area of 2116 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 54 must be divided to get a perfect square?
  33. 33.A square garden has an area of 529 square m. How long is each side (in m)?
  34. 34.What is 59²? =
  35. 35.What is 16²? =
  36. 36.How many whole numbers lie between 13² and 14²?
  37. 37.What is the smallest whole number by which 50 must be divided to get a perfect square?
  38. 38.What is the smallest whole number by which 52 must be divided to get a perfect square?
  39. 39.How many whole numbers lie between 18² and 19²?
  40. 40.What is √7396? =

Answer key

  1. 12
  2. 841
  3. 625
  4. 5929
  5. 361
  6. 15
  7. 37
  8. 14
  9. 11
  10. 46
  11. 76
  12. 625
  13. 18
  14. 3600
  15. 10
  16. 4761
  17. 23
  18. 29
  19. 5776
  20. 2
  21. 576
  22. 45
  23. 6
  24. 676
  25. 34
  26. 961
  27. 100
  28. 1156
  29. 7225
  30. 484
  31. 46
  32. 6
  33. 23
  34. 3481
  35. 256
  36. 26
  37. 2
  38. 13
  39. 36
  40. 86

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