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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 504 · 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 the smallest whole number by which 1053 must be divided to get a perfect square?
  2. 2.What is √625? =
  3. 3.Which of these is a perfect square? (a) 1225 (b) 1228 (c) 1278
  4. 4.How many whole numbers lie between 32² and 33²?
  5. 5.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  6. 6.How many whole numbers lie between 10² and 11²?
  7. 7.What is the smallest whole number by which 40 must be divided to get a perfect square?
  8. 8.How many whole numbers lie between 13² and 14²?
  9. 9.What is the smallest whole number by which 32 must be divided to get a perfect square?
  10. 10.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is 61²? =
  13. 13.A square garden has an area of 169 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 196 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 225 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 16² and 17²?
  17. 17.Which of these is a perfect square? (a) 289 (b) 314 (c) 321
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 98 must be divided to get a perfect square?
  20. 20.What is the smallest whole number by which 250 must be divided to get a perfect square?
  21. 21.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
  22. 22.What is 28²? =
  23. 23.What is the smallest whole number by which 20 must be divided to get a perfect square?
  24. 24.A square garden has an area of 484 square m. How long is each side (in m)?
  25. 25.What is √2025? =
  26. 26.What is 11²? =
  27. 27.Which of these is a perfect square? (a) 1147 (b) 1089 (c) 1123
  28. 28.What is √361? =
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √196? =
  31. 31.How many whole numbers lie between 8² and 9²?
  32. 32.A square garden has an area of 3481 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 832 must be divided to get a perfect square?
  34. 34.What is 12²? =
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  36. 36.A square garden has an area of 81 square m. How long is each side (in m)?
  37. 37.What is 83²? =
  38. 38.A square garden has an area of 36 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 576 square m. How long is each side (in m)?
  40. 40.What is 56²? =

Answer key

  1. 13
  2. 25
  3. 1225
  4. 64
  5. 2
  6. 20
  7. 10
  8. 26
  9. 2
  10. 2
  11. 25
  12. 3721
  13. 13
  14. 14
  15. 15
  16. 32
  17. 289
  18. 841
  19. 2
  20. 10
  21. 13
  22. 784
  23. 5
  24. 22
  25. 45
  26. 121
  27. 1089
  28. 19
  29. 256
  30. 14
  31. 16
  32. 59
  33. 13
  34. 144
  35. 196
  36. 9
  37. 6889
  38. 6
  39. 24
  40. 3136

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