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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 36 · 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 441 square m. How long is each side (in m)?
  2. 2.What is 47²? =
  3. 3.How many whole numbers lie between 26² and 27²?
  4. 4.What is the smallest whole number by which 175 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 303 (b) 321 (c) 289
  6. 6.What is 15²? =
  7. 7.A square garden has an area of 3136 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 159 (b) 145 (c) 144
  9. 9.How many whole numbers lie between 12² and 13²?
  10. 10.Which of these is a perfect square? (a) 1604 (b) 1643 (c) 1600
  11. 11.What is √400? =
  12. 12.What is the smallest whole number by which 243 must be divided to get a perfect square?
  13. 13.A square garden has an area of 196 square m. How long is each side (in m)?
  14. 14.What is 36²? =
  15. 15.A square garden has an area of 2916 square m. How long is each side (in m)?
  16. 16.What is √841? =
  17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  19. 19.What is √1024? =
  20. 20.What is √441? =
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 48 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 36² and 37²?
  24. 24.What is √6561? =
  25. 25.Which of these is a perfect square? (a) 169 (b) 187 (c) 179
  26. 26.What is 31²? =
  27. 27.What is the smallest whole number by which 60 must be divided to get a perfect square?
  28. 28.A square garden has an area of 36 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 13² and 14²?
  30. 30.What is 88²? =
  31. 31.How many whole numbers lie between 49² and 50²?
  32. 32.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  33. 33.A square garden has an area of 529 square m. How long is each side (in m)?
  34. 34.A square garden has an area of 25 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 180 must be divided to get a perfect square?
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 84²? =
  40. 40.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 21
  2. 2209
  3. 52
  4. 7
  5. 289
  6. 225
  7. 56
  8. 144
  9. 24
  10. 1600
  11. 20
  12. 3
  13. 14
  14. 1296
  15. 54
  16. 29
  17. 361
  18. 7
  19. 32
  20. 21
  21. 576
  22. 3
  23. 72
  24. 81
  25. 169
  26. 961
  27. 15
  28. 6
  29. 26
  30. 7744
  31. 98
  32. 5
  33. 23
  34. 5
  35. 6
  36. 441
  37. 5
  38. 144
  39. 7056
  40. 256

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