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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 149 · 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 √2304? =
  2. 2.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 63²? =
  5. 5.What is 91²? =
  6. 6.What is the smallest whole number by which 52 must be divided to get a perfect square?
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √6084? =
  9. 9.What is 19²? =
  10. 10.What is √961? =
  11. 11.How many whole numbers lie between 32² and 33²?
  12. 12.What is √5929? =
  13. 13.How many whole numbers lie between 49² and 50²?
  14. 14.A square garden has an area of 1089 square m. How long is each side (in m)?
  15. 15.What is √7225? =
  16. 16.Which of these is a perfect square? (a) 100 (b) 107 (c) 110
  17. 17.What is 88²? =
  18. 18.How many whole numbers lie between 18² and 19²?
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  21. 21.A square garden has an area of 3481 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 1296 (b) 1303 (c) 1305
  23. 23.What is the smallest whole number by which 12 must be divided to get a perfect square?
  24. 24.What is √1156? =
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 3136 square m. How long is each side (in m)?
  27. 27.What is √3969? =
  28. 28.Which of these is a perfect square? (a) 1024 (b) 1039 (c) 1037
  29. 29.What is the smallest whole number by which 112 must be divided to get a perfect square?
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  31. 31.How many whole numbers lie between 39² and 40²?
  32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 1521 (b) 1544 (c) 1522
  34. 34.What is 98²? =
  35. 35.What is √4761? =
  36. 36.What is 58²? =
  37. 37.How many whole numbers lie between 40² and 41²?
  38. 38.A square garden has an area of 36 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 46² and 47²?
  40. 40.What is √9801? =

Answer key

  1. 48
  2. 13
  3. 900
  4. 3969
  5. 8281
  6. 13
  7. 49
  8. 78
  9. 361
  10. 31
  11. 64
  12. 77
  13. 98
  14. 33
  15. 85
  16. 100
  17. 7744
  18. 36
  19. 81
  20. 6
  21. 59
  22. 1296
  23. 3
  24. 34
  25. 625
  26. 56
  27. 63
  28. 1024
  29. 7
  30. 324
  31. 78
  32. 64
  33. 1521
  34. 9604
  35. 69
  36. 3364
  37. 80
  38. 6
  39. 92
  40. 99

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