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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 469 · 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.What is the smallest whole number by which 117 must be divided to get a perfect square?
  2. 2.What is √4096? =
  3. 3.What is the smallest whole number by which 90 must be divided to get a perfect square?
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is 48²? =
  7. 7.What is √196? =
  8. 8.What is 33²? =
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 916 (b) 941 (c) 900
  11. 11.What is the smallest whole number by which 45 must be divided to get a perfect square?
  12. 12.What is 74²? =
  13. 13.Which of these is a perfect square? (a) 1392 (b) 1369 (c) 1383
  14. 14.What is the smallest whole number by which 128 must be divided to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 1627 (b) 1600 (c) 1668
  16. 16.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  17. 17.What is 12²? =
  18. 18.What is √3136? =
  19. 19.Which of these is a perfect square? (a) 1058 (b) 1024 (c) 1080
  20. 20.Which of these is a perfect square? (a) 651 (b) 660 (c) 625
  21. 21.What is 16²? =
  22. 22.A square garden has an area of 1764 square m. How long is each side (in m)?
  23. 23.A square garden has an area of 1024 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 613 (b) 576 (c) 600
  25. 25.What is √9409? =
  26. 26.A square garden has an area of 289 square m. How long is each side (in m)?
  27. 27.What is √6084? =
  28. 28.What is √9216? =
  29. 29.What is 62²? =
  30. 30.A square garden has an area of 144 square m. How long is each side (in m)?
  31. 31.What is √5476? =
  32. 32.How many whole numbers lie between 8² and 9²?
  33. 33.How many whole numbers lie between 47² and 48²?
  34. 34.Which of these is a perfect square? (a) 962 (b) 1018 (c) 961
  35. 35.What is √8281? =
  36. 36.Which of these is a perfect square? (a) 371 (b) 384 (c) 361
  37. 37.Which of these is a perfect square? (a) 289 (b) 297 (c) 321
  38. 38.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  39. 39.What is 18²? =
  40. 40.Which of these is a perfect square? (a) 478 (b) 455 (c) 441

Answer key

  1. 13
  2. 64
  3. 10
  4. 64
  5. 81
  6. 2304
  7. 14
  8. 1089
  9. 169
  10. 900
  11. 5
  12. 5476
  13. 1369
  14. 2
  15. 1600
  16. 7
  17. 144
  18. 56
  19. 1024
  20. 625
  21. 256
  22. 42
  23. 32
  24. 576
  25. 97
  26. 17
  27. 78
  28. 96
  29. 3844
  30. 12
  31. 74
  32. 16
  33. 94
  34. 961
  35. 91
  36. 361
  37. 289
  38. 10
  39. 324
  40. 441

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