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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 428 · 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 900 square m. How long is each side (in m)?
  2. 2.What is √3249? =
  3. 3.How many whole numbers lie between 35² and 36²?
  4. 4.Which of these is a perfect square? (a) 144 (b) 148 (c) 156
  5. 5.How many whole numbers lie between 22² and 23²?
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 11² and 12²?
  8. 8.A square garden has an area of 1156 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 863 (b) 841 (c) 849
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 46² and 47²?
  12. 12.What is √3844? =
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 92²? =
  15. 15.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  16. 16.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is the smallest whole number by which 135 must be divided to get a perfect square?
  18. 18.What is √1024? =
  19. 19.What is 30²? =
  20. 20.Which of these is a perfect square? (a) 256 (b) 274 (c) 267
  21. 21.How many whole numbers lie between 24² and 25²?
  22. 22.What is √324? =
  23. 23.A square garden has an area of 2025 square m. How long is each side (in m)?
  24. 24.What is √9409? =
  25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is √289? =
  27. 27.What is 84²? =
  28. 28.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  29. 29.What is 47²? =
  30. 30.Which of these is a perfect square? (a) 115 (b) 109 (c) 100
  31. 31.What is √2304? =
  32. 32.Which of these is a perfect square? (a) 390 (b) 395 (c) 361
  33. 33.What is 16²? =
  34. 34.Which of these is a perfect square? (a) 584 (b) 576 (c) 624
  35. 35.Which of these is a perfect square? (a) 914 (b) 960 (c) 900
  36. 36.A square garden has an area of 1444 square m. How long is each side (in m)?
  37. 37.What is √8836? =
  38. 38.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  39. 39.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  40. 40.A square garden has an area of 2304 square m. How long is each side (in m)?

Answer key

  1. 30
  2. 57
  3. 70
  4. 144
  5. 44
  6. 36
  7. 22
  8. 34
  9. 841
  10. 529
  11. 92
  12. 62
  13. 900
  14. 8464
  15. 3
  16. 841
  17. 15
  18. 32
  19. 900
  20. 256
  21. 48
  22. 18
  23. 45
  24. 97
  25. 64
  26. 17
  27. 7056
  28. 3
  29. 2209
  30. 100
  31. 48
  32. 361
  33. 256
  34. 576
  35. 900
  36. 38
  37. 94
  38. 13
  39. 6
  40. 48

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