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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 491 · 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 1225 square m. How long is each side (in m)?
  2. 2.What is 57²? =
  3. 3.What is the smallest whole number by which 117 must be divided to get a perfect square?
  4. 4.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is √484? =
  8. 8.What is 24²? =
  9. 9.How many whole numbers lie between 7² and 8²?
  10. 10.Which of these is a perfect square? (a) 392 (b) 361 (c) 380
  11. 11.A square garden has an area of 1681 square m. How long is each side (in m)?
  12. 12.What is 77²? =
  13. 13.Which of these is a perfect square? (a) 729 (b) 767 (c) 761
  14. 14.A square garden has an area of 64 square m. How long is each side (in m)?
  15. 15.What is 81²? =
  16. 16.How many whole numbers lie between 45² and 46²?
  17. 17.What is √5041? =
  18. 18.Which of these is a perfect square? (a) 961 (b) 977 (c) 1023
  19. 19.What is √4489? =
  20. 20.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 202 (b) 201 (c) 196
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 54 must be divided to get a perfect square?
  25. 25.A square garden has an area of 1444 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 1664 (b) 1619 (c) 1600
  27. 27.What is √2500? =
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 11²? =
  30. 30.How many whole numbers lie between 50² and 51²?
  31. 31.A square garden has an area of 1849 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  33. 33.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is 58²? =
  36. 36.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  37. 37.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 83²? =
  40. 40.What is the smallest whole number by which 540 must be multiplied to get a perfect square?

Answer key

  1. 35
  2. 3249
  3. 13
  4. 5
  5. 441
  6. 169
  7. 22
  8. 576
  9. 14
  10. 361
  11. 41
  12. 5929
  13. 729
  14. 8
  15. 6561
  16. 90
  17. 71
  18. 961
  19. 67
  20. 196
  21. 11
  22. 196
  23. 100
  24. 6
  25. 38
  26. 1600
  27. 50
  28. 625
  29. 121
  30. 100
  31. 43
  32. 14
  33. 7
  34. 49
  35. 3364
  36. 14
  37. 2
  38. 36
  39. 6889
  40. 15

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