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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 438 · 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 18² and 19²?
  2. 2.Which of these is a perfect square? (a) 441 (b) 470 (c) 482
  3. 3.What is the smallest whole number by which 343 must be divided to get a perfect square?
  4. 4.A square garden has an area of 144 square m. How long is each side (in m)?
  5. 5.What is √1369? =
  6. 6.Which of these is a perfect square? (a) 545 (b) 529 (c) 538
  7. 7.What is √1225? =
  8. 8.A square garden has an area of 2809 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 160 must be divided to get a perfect square?
  10. 10.A square garden has an area of 324 square m. How long is each side (in m)?
  11. 11.Which of these is a perfect square? (a) 305 (b) 289 (c) 306
  12. 12.What is 98²? =
  13. 13.Which of these is a perfect square? (a) 123 (b) 121 (c) 138
  14. 14.What is √3844? =
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 6² and 7²?
  17. 17.What is the smallest whole number by which 32 must be divided to get a perfect square?
  18. 18.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  19. 19.What is √484? =
  20. 20.What is 73²? =
  21. 21.Which of these is a perfect square? (a) 145 (b) 161 (c) 144
  22. 22.What is 94²? =
  23. 23.What is √676? =
  24. 24.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  25. 25.What is the smallest whole number by which 150 must be divided to get a perfect square?
  26. 26.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  27. 27.What is 43²? =
  28. 28.What is √9801? =
  29. 29.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  30. 30.What is 78²? =
  31. 31.What is √6724? =
  32. 32.What is the smallest whole number by which 60 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 42² and 43²?
  34. 34.How many whole numbers lie between 21² and 22²?
  35. 35.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 735 must be divided to get a perfect square?
  37. 37.A square garden has an area of 2116 square m. How long is each side (in m)?
  38. 38.What is 49²? =
  39. 39.What is 63²? =
  40. 40.Which of these is a perfect square? (a) 620 (b) 617 (c) 576

Answer key

  1. 36
  2. 441
  3. 7
  4. 12
  5. 37
  6. 529
  7. 35
  8. 53
  9. 10
  10. 18
  11. 289
  12. 9604
  13. 121
  14. 62
  15. 256
  16. 12
  17. 2
  18. 13
  19. 22
  20. 5329
  21. 144
  22. 8836
  23. 26
  24. 11
  25. 6
  26. 14
  27. 1849
  28. 99
  29. 7
  30. 6084
  31. 82
  32. 15
  33. 84
  34. 42
  35. 7
  36. 15
  37. 46
  38. 2401
  39. 3969
  40. 576

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