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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 157 · 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.What is √1156? =
  2. 2.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  5. 5.A square garden has an area of 2916 square m. How long is each side (in m)?
  6. 6.What is √5184? =
  7. 7.How many whole numbers lie between 43² and 44²?
  8. 8.What is √1024? =
  9. 9.A square garden has an area of 441 square m. How long is each side (in m)?
  10. 10.What is √529? =
  11. 11.Which of these is a perfect square? (a) 216 (b) 205 (c) 196
  12. 12.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  13. 13.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √3364? =
  17. 17.What is the smallest whole number by which 63 must be divided to get a perfect square?
  18. 18.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  19. 19.A square garden has an area of 361 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 961 (b) 964 (c) 986
  21. 21.How many whole numbers lie between 17² and 18²?
  22. 22.A square garden has an area of 2209 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 109 (b) 100 (c) 102
  26. 26.A square garden has an area of 3025 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 6² and 7²?
  28. 28.How many whole numbers lie between 22² and 23²?
  29. 29.What is √484? =
  30. 30.A square garden has an area of 900 square m. How long is each side (in m)?
  31. 31.What is √3844? =
  32. 32.A square garden has an area of 49 square m. How long is each side (in m)?
  33. 33.What is √256? =
  34. 34.What is 25²? =
  35. 35.Which of these is a perfect square? (a) 531 (b) 562 (c) 529
  36. 36.How many whole numbers lie between 25² and 26²?
  37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  38. 38.A square garden has an area of 225 square m. How long is each side (in m)?
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is 12²? =

Answer key

  1. 34
  2. 13
  3. 81
  4. 3
  5. 54
  6. 72
  7. 86
  8. 32
  9. 21
  10. 23
  11. 196
  12. 2
  13. 10
  14. 64
  15. 121
  16. 58
  17. 7
  18. 36
  19. 19
  20. 961
  21. 34
  22. 47
  23. 841
  24. 7
  25. 100
  26. 55
  27. 12
  28. 44
  29. 22
  30. 30
  31. 62
  32. 7
  33. 16
  34. 625
  35. 529
  36. 50
  37. 576
  38. 15
  39. 529
  40. 144

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