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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 170 · 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 448 must be divided to get a perfect square?
  2. 2.A square garden has an area of 2401 square m. How long is each side (in m)?
  3. 3.A square garden has an area of 2500 square m. How long is each side (in m)?
  4. 4.Which of these is a perfect square? (a) 121 (b) 133 (c) 132
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 2304 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 390 (b) 361 (c) 373
  8. 8.How many whole numbers lie between 39² and 40²?
  9. 9.How many whole numbers lie between 16² and 17²?
  10. 10.Which of these is a perfect square? (a) 316 (b) 289 (c) 292
  11. 11.What is √9409? =
  12. 12.What is √5329? =
  13. 13.What is 57²? =
  14. 14.A square garden has an area of 3481 square m. How long is each side (in m)?
  15. 15.What is √484? =
  16. 16.What is the smallest whole number by which 243 must be divided to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1163 (b) 1165 (c) 1156
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is √1225? =
  20. 20.What is 82²? =
  21. 21.What is √441? =
  22. 22.What is √9025? =
  23. 23.Which of these is a perfect square? (a) 961 (b) 979 (c) 999
  24. 24.What is 11²? =
  25. 25.How many whole numbers lie between 37² and 38²?
  26. 26.A square garden has an area of 676 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  28. 28.What is √144? =
  29. 29.Which of these is a perfect square? (a) 1435 (b) 1369 (c) 1395
  30. 30.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  31. 31.What is √3249? =
  32. 32.A square garden has an area of 900 square m. How long is each side (in m)?
  33. 33.What is 69²? =
  34. 34.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 729 square m. How long is each side (in m)?
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 48² and 49²?
  40. 40.A square garden has an area of 3136 square m. How long is each side (in m)?

Answer key

  1. 7
  2. 49
  3. 50
  4. 121
  5. 841
  6. 48
  7. 361
  8. 78
  9. 32
  10. 289
  11. 97
  12. 73
  13. 3249
  14. 59
  15. 22
  16. 3
  17. 1156
  18. 676
  19. 35
  20. 6724
  21. 21
  22. 95
  23. 961
  24. 121
  25. 74
  26. 26
  27. 10
  28. 12
  29. 1369
  30. 14
  31. 57
  32. 30
  33. 4761
  34. 2
  35. 121
  36. 49
  37. 27
  38. 25
  39. 96
  40. 56

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