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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 472 · 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.Which of these is a perfect square? (a) 134 (b) 131 (c) 121
  2. 2.What is √625? =
  3. 3.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  4. 4.A square garden has an area of 625 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  6. 6.What is 44²? =
  7. 7.What is the smallest whole number by which 12 must be divided to get a perfect square?
  8. 8.A square garden has an area of 81 square m. How long is each side (in m)?
  9. 9.A square garden has an area of 3481 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  11. 11.What is √7225? =
  12. 12.What is the smallest whole number by which 243 must be divided to get a perfect square?
  13. 13.How many whole numbers lie between 18² and 19²?
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √5041? =
  16. 16.What is √9025? =
  17. 17.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  18. 18.What is 70²? =
  19. 19.How many whole numbers lie between 41² and 42²?
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is √1521? =
  23. 23.What is the smallest whole number by which 117 must be divided to get a perfect square?
  24. 24.What is √1600? =
  25. 25.What is 94²? =
  26. 26.What is √4489? =
  27. 27.A square garden has an area of 1764 square m. How long is each side (in m)?
  28. 28.What is √5184? =
  29. 29.Which of these is a perfect square? (a) 1160 (b) 1167 (c) 1156
  30. 30.A square garden has an area of 36 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  32. 32.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 408 (b) 400 (c) 412
  34. 34.What is √7569? =
  35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 961 (b) 1015 (c) 982
  37. 37.What is √3136? =
  38. 38.A square garden has an area of 2304 square m. How long is each side (in m)?
  39. 39.What is √4225? =
  40. 40.Which of these is a perfect square? (a) 593 (b) 611 (c) 576

Answer key

  1. 121
  2. 25
  3. 15
  4. 25
  5. 10
  6. 1936
  7. 3
  8. 9
  9. 59
  10. 3
  11. 85
  12. 3
  13. 36
  14. 144
  15. 71
  16. 95
  17. 13
  18. 4900
  19. 82
  20. 49
  21. 441
  22. 39
  23. 13
  24. 40
  25. 8836
  26. 67
  27. 42
  28. 72
  29. 1156
  30. 6
  31. 3
  32. 14
  33. 400
  34. 87
  35. 576
  36. 961
  37. 56
  38. 48
  39. 65
  40. 576

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