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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 143 · 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 12 must be multiplied to get a perfect square?
  2. 2.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 225 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.Which of these is a perfect square? (a) 100 (b) 101 (c) 118
  6. 6.What is 44²? =
  7. 7.What is √5184? =
  8. 8.What is √3481? =
  9. 9.A square garden has an area of 529 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  11. 11.How many whole numbers lie between 29² and 30²?
  12. 12.A square garden has an area of 1369 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 361 square m. How long is each side (in m)?
  14. 14.What is √6724? =
  15. 15.A square garden has an area of 2116 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is √6561? =
  18. 18.What is √6400? =
  19. 19.What is √6889? =
  20. 20.A square garden has an area of 1089 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 250 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1250 (b) 1225 (c) 1286
  23. 23.Which of these is a perfect square? (a) 1488 (b) 1517 (c) 1444
  24. 24.What is √3721? =
  25. 25.Which of these is a perfect square? (a) 690 (b) 723 (c) 676
  26. 26.How many whole numbers lie between 7² and 8²?
  27. 27.What is 74²? =
  28. 28.What is √2209? =
  29. 29.A square garden has an area of 144 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 495 (b) 484 (c) 494
  31. 31.What is 19²? =
  32. 32.How many whole numbers lie between 50² and 51²?
  33. 33.A square garden has an area of 400 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 27² and 28²?
  35. 35.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  36. 36.What is √3025? =
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 36² and 37²?

Answer key

  1. 3
  2. 14
  3. 15
  4. 25
  5. 100
  6. 1936
  7. 72
  8. 59
  9. 23
  10. 7
  11. 58
  12. 37
  13. 19
  14. 82
  15. 46
  16. 441
  17. 81
  18. 80
  19. 83
  20. 33
  21. 10
  22. 1225
  23. 1444
  24. 61
  25. 676
  26. 14
  27. 5476
  28. 47
  29. 12
  30. 484
  31. 361
  32. 100
  33. 20
  34. 54
  35. 2
  36. 55
  37. 324
  38. 3
  39. 11
  40. 72

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