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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 534 · 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 √196? =
  2. 2.Which of these is a perfect square? (a) 1522 (b) 1545 (c) 1521
  3. 3.Which of these is a perfect square? (a) 1356 (b) 1352 (c) 1296
  4. 4.What is 50²? =
  5. 5.What is √1764? =
  6. 6.A square garden has an area of 361 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  10. 10.What is √729? =
  11. 11.What is the smallest whole number by which 108 must be divided to get a perfect square?
  12. 12.What is 48²? =
  13. 13.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 26² and 27²?
  15. 15.What is 72²? =
  16. 16.How many whole numbers lie between 19² and 20²?
  17. 17.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  20. 20.What is 31²? =
  21. 21.A square garden has an area of 841 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 784 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 36² and 37²?
  24. 24.A square garden has an area of 1936 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 16² and 17²?
  26. 26.What is 40²? =
  27. 27.A square garden has an area of 1024 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 3136 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 9² and 10²?
  30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  32. 32.A square garden has an area of 36 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 64 square m. How long is each side (in m)?
  34. 34.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  35. 35.How many whole numbers lie between 25² and 26²?
  36. 36.What is √6241? =
  37. 37.What is the smallest whole number by which 60 must be divided to get a perfect square?
  38. 38.What is 69²? =
  39. 39.A square garden has an area of 324 square m. How long is each side (in m)?
  40. 40.What is 65²? =

Answer key

  1. 14
  2. 1521
  3. 1296
  4. 2500
  5. 42
  6. 19
  7. 9
  8. 7
  9. 11
  10. 27
  11. 3
  12. 2304
  13. 15
  14. 52
  15. 5184
  16. 38
  17. 11
  18. 81
  19. 6
  20. 961
  21. 29
  22. 28
  23. 72
  24. 44
  25. 32
  26. 1600
  27. 32
  28. 56
  29. 18
  30. 361
  31. 25
  32. 6
  33. 8
  34. 2
  35. 50
  36. 79
  37. 15
  38. 4761
  39. 18
  40. 4225

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