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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 207 · 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 529 square m. How long is each side (in m)?
  2. 2.What is 51²? =
  3. 3.What is the smallest whole number by which 135 must be divided to get a perfect square?
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 1444 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 800 (b) 793 (c) 784
  8. 8.What is the smallest whole number by which 28 must be divided to get a perfect square?
  9. 9.What is √4900? =
  10. 10.A square garden has an area of 441 square m. How long is each side (in m)?
  11. 11.What is √8836? =
  12. 12.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  13. 13.What is √3364? =
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 33²? =
  16. 16.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
  17. 17.What is 87²? =
  18. 18.What is √4225? =
  19. 19.What is √2401? =
  20. 20.What is the smallest whole number by which 176 must be divided to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 961 (b) 985 (c) 991
  22. 22.Which of these is a perfect square? (a) 114 (b) 100 (c) 117
  23. 23.What is √7056? =
  24. 24.A square garden has an area of 121 square m. How long is each side (in m)?
  25. 25.What is 28²? =
  26. 26.A square garden has an area of 2809 square m. How long is each side (in m)?
  27. 27.Which of these is a perfect square? (a) 1075 (b) 1063 (c) 1024
  28. 28.How many whole numbers lie between 17² and 18²?
  29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √1024? =
  31. 31.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 57²? =
  33. 33.What is √2025? =
  34. 34.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 73²? =
  37. 37.What is the smallest whole number by which 98 must be divided to get a perfect square?
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √5476? =
  40. 40.What is the smallest whole number by which 150 must be divided to get a perfect square?

Answer key

  1. 23
  2. 2601
  3. 15
  4. 576
  5. 3
  6. 38
  7. 784
  8. 7
  9. 70
  10. 21
  11. 94
  12. 3
  13. 58
  14. 100
  15. 1089
  16. 7
  17. 7569
  18. 65
  19. 49
  20. 11
  21. 961
  22. 100
  23. 84
  24. 11
  25. 784
  26. 53
  27. 1024
  28. 34
  29. 144
  30. 32
  31. 529
  32. 3249
  33. 45
  34. 13
  35. 25
  36. 5329
  37. 2
  38. 289
  39. 74
  40. 6

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