← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 471 · 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 72 must be multiplied to get a perfect square?
  2. 2.What is 43²? =
  3. 3.How many whole numbers lie between 39² and 40²?
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 14² and 15²?
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is 80²? =
  8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √5041? =
  10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the smallest whole number by which 448 must be divided to get a perfect square?
  12. 12.Which of these is a perfect square? (a) 196 (b) 210 (c) 211
  13. 13.Which of these is a perfect square? (a) 1589 (b) 1575 (c) 1521
  14. 14.What is √5776? =
  15. 15.A square garden has an area of 625 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 175 must be divided to get a perfect square?
  17. 17.How many whole numbers lie between 21² and 22²?
  18. 18.A square garden has an area of 900 square m. How long is each side (in m)?
  19. 19.What is √3025? =
  20. 20.A square garden has an area of 2809 square m. How long is each side (in m)?
  21. 21.What is √324? =
  22. 22.Which of these is a perfect square? (a) 729 (b) 768 (c) 765
  23. 23.Which of these is a perfect square? (a) 397 (b) 390 (c) 361
  24. 24.What is 25²? =
  25. 25.What is 93²? =
  26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the smallest whole number by which 80 must be divided to get a perfect square?
  28. 28.What is 58²? =
  29. 29.What is √484? =
  30. 30.Which of these is a perfect square? (a) 958 (b) 900 (c) 923
  31. 31.A square garden has an area of 1764 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 735 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 17² and 18²?
  34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the smallest whole number by which 150 must be divided to get a perfect square?
  36. 36.What is √1849? =
  37. 37.What is √784? =
  38. 38.What is the smallest whole number by which 810 must be divided to get a perfect square?
  39. 39.What is 18²? =
  40. 40.What is the smallest whole number by which 275 must be multiplied to get a perfect square?

Answer key

  1. 2
  2. 1849
  3. 78
  4. 121
  5. 28
  6. 81
  7. 6400
  8. 324
  9. 71
  10. 841
  11. 7
  12. 196
  13. 1521
  14. 76
  15. 25
  16. 7
  17. 42
  18. 30
  19. 55
  20. 53
  21. 18
  22. 729
  23. 361
  24. 625
  25. 8649
  26. 441
  27. 5
  28. 3364
  29. 22
  30. 900
  31. 42
  32. 15
  33. 34
  34. 256
  35. 6
  36. 43
  37. 28
  38. 10
  39. 324
  40. 11

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets