← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 49 · 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 77²? =
  2. 2.What is √3364? =
  3. 3.What is √1521? =
  4. 4.What is √1600? =
  5. 5.How many whole numbers lie between 11² and 12²?
  6. 6.How many whole numbers lie between 41² and 42²?
  7. 7.What is the smallest whole number by which 45 must be divided to get a perfect square?
  8. 8.What is 60²? =
  9. 9.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 25² and 26²?
  11. 11.What is √9801? =
  12. 12.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 484 (b) 507 (c) 497
  14. 14.Which of these is a perfect square? (a) 657 (b) 655 (c) 625
  15. 15.A square garden has an area of 81 square m. How long is each side (in m)?
  16. 16.What is 42²? =
  17. 17.Which of these is a perfect square? (a) 604 (b) 576 (c) 605
  18. 18.What is the smallest whole number by which 490 must be divided to get a perfect square?
  19. 19.What is √900? =
  20. 20.What is √225? =
  21. 21.How many whole numbers lie between 43² and 44²?
  22. 22.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √361? =
  24. 24.What is 12²? =
  25. 25.What is the smallest whole number by which 112 must be divided to get a perfect square?
  26. 26.Which of these is a perfect square? (a) 1617 (b) 1674 (c) 1600
  27. 27.What is the smallest whole number by which 160 must be divided to get a perfect square?
  28. 28.How many whole numbers lie between 29² and 30²?
  29. 29.Which of these is a perfect square? (a) 1382 (b) 1369 (c) 1433
  30. 30.What is the smallest whole number by which 56 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 1304 (b) 1296 (c) 1300
  32. 32.What is the smallest whole number by which 250 must be divided to get a perfect square?
  33. 33.A square garden has an area of 900 square m. How long is each side (in m)?
  34. 34.A square garden has an area of 1936 square m. How long is each side (in m)?
  35. 35.What is the smallest whole number by which 486 must be divided to get a perfect square?
  36. 36.What is 61²? =
  37. 37.What is √3025? =
  38. 38.What is 73²? =
  39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
  40. 40.How many whole numbers lie between 18² and 19²?

Answer key

  1. 5929
  2. 58
  3. 39
  4. 40
  5. 22
  6. 82
  7. 5
  8. 3600
  9. 2
  10. 50
  11. 99
  12. 14
  13. 484
  14. 625
  15. 9
  16. 1764
  17. 576
  18. 10
  19. 30
  20. 15
  21. 86
  22. 625
  23. 19
  24. 144
  25. 7
  26. 1600
  27. 10
  28. 58
  29. 1369
  30. 14
  31. 1296
  32. 10
  33. 30
  34. 44
  35. 6
  36. 3721
  37. 55
  38. 5329
  39. 15
  40. 36

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