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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 269 · 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 96²? =
  2. 2.A square garden has an area of 64 square m. How long is each side (in m)?
  3. 3.What is 13²? =
  4. 4.What is 95²? =
  5. 5.What is the smallest whole number by which 891 must be divided to get a perfect square?
  6. 6.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  7. 7.What is 21²? =
  8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 484 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 41² and 42²?
  13. 13.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 2500 square m. How long is each side (in m)?
  16. 16.What is 62²? =
  17. 17.What is √9409? =
  18. 18.What is √729? =
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  22. 22.How many whole numbers lie between 10² and 11²?
  23. 23.What is the smallest whole number by which 208 must be divided to get a perfect square?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.How many whole numbers lie between 13² and 14²?
  26. 26.Which of these is a perfect square? (a) 1296 (b) 1330 (c) 1322
  27. 27.What is 85²? =
  28. 28.What is √5041? =
  29. 29.How many whole numbers lie between 12² and 13²?
  30. 30.What is 71²? =
  31. 31.A square garden has an area of 441 square m. How long is each side (in m)?
  32. 32.Which of these is a perfect square? (a) 1369 (b) 1397 (c) 1373
  33. 33.What is √1521? =
  34. 34.A square garden has an area of 1156 square m. How long is each side (in m)?
  35. 35.What is √4761? =
  36. 36.What is 51²? =
  37. 37.A square garden has an area of 3481 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 49 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 1521 (b) 1552 (c) 1553
  40. 40.What is the smallest whole number by which 468 must be multiplied to get a perfect square?

Answer key

  1. 9216
  2. 8
  3. 169
  4. 9025
  5. 11
  6. 6
  7. 441
  8. 289
  9. 3
  10. 625
  11. 22
  12. 82
  13. 14
  14. 729
  15. 50
  16. 3844
  17. 97
  18. 27
  19. 841
  20. 11
  21. 100
  22. 20
  23. 13
  24. 64
  25. 26
  26. 1296
  27. 7225
  28. 71
  29. 24
  30. 5041
  31. 21
  32. 1369
  33. 39
  34. 34
  35. 69
  36. 2601
  37. 59
  38. 7
  39. 1521
  40. 13

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