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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 328 · 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 sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 380 (b) 361 (c) 378
  3. 3.What is √324? =
  4. 4.A square garden has an area of 1156 square m. How long is each side (in m)?
  5. 5.What is 22²? =
  6. 6.Which of these is a perfect square? (a) 1225 (b) 1293 (c) 1248
  7. 7.How many whole numbers lie between 14² and 15²?
  8. 8.A square garden has an area of 2116 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 31² and 32²?
  10. 10.A square garden has an area of 2601 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 328 (b) 352 (c) 324
  13. 13.How many whole numbers lie between 46² and 47²?
  14. 14.What is 30²? =
  15. 15.What is the smallest whole number by which 160 must be divided to get a perfect square?
  16. 16.A square garden has an area of 676 square m. How long is each side (in m)?
  17. 17.What is 46²? =
  18. 18.What is 93²? =
  19. 19.What is the smallest whole number by which 18 must be divided to get a perfect square?
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  21. 21.A square garden has an area of 625 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 2025 square m. How long is each side (in m)?
  23. 23.What is 67²? =
  24. 24.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  25. 25.How many whole numbers lie between 9² and 10²?
  26. 26.Which of these is a perfect square? (a) 541 (b) 529 (c) 540
  27. 27.How many whole numbers lie between 47² and 48²?
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 15²? =
  30. 30.What is √8836? =
  31. 31.What is √5476? =
  32. 32.What is 83²? =
  33. 33.Which of these is a perfect square? (a) 900 (b) 951 (c) 905
  34. 34.What is 62²? =
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 278 (b) 256 (c) 273
  37. 37.A square garden has an area of 100 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 289 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 98 must be divided to get a perfect square?

Answer key

  1. 25
  2. 361
  3. 18
  4. 34
  5. 484
  6. 1225
  7. 28
  8. 46
  9. 62
  10. 51
  11. 2
  12. 324
  13. 92
  14. 900
  15. 10
  16. 26
  17. 2116
  18. 8649
  19. 2
  20. 100
  21. 25
  22. 45
  23. 4489
  24. 15
  25. 18
  26. 529
  27. 94
  28. 144
  29. 225
  30. 94
  31. 74
  32. 6889
  33. 900
  34. 3844
  35. 196
  36. 256
  37. 10
  38. 17
  39. 14
  40. 2

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