← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 399 · 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.How many whole numbers lie between 24² and 25²?
  2. 2.How many whole numbers lie between 27² and 28²?
  3. 3.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  4. 4.What is √1521? =
  5. 5.What is 17²? =
  6. 6.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 224 (b) 220 (c) 196
  8. 8.How many whole numbers lie between 45² and 46²?
  9. 9.What is √1156? =
  10. 10.How many whole numbers lie between 48² and 49²?
  11. 11.What is 87²? =
  12. 12.A square garden has an area of 81 square m. How long is each side (in m)?
  13. 13.What is 38²? =
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 829 (b) 797 (c) 784
  16. 16.What is √576? =
  17. 17.Which of these is a perfect square? (a) 1354 (b) 1296 (c) 1299
  18. 18.How many whole numbers lie between 26² and 27²?
  19. 19.What is √2809? =
  20. 20.What is 15²? =
  21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 144 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 246 (b) 225 (c) 232
  24. 24.What is 59²? =
  25. 25.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 45 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 1619 (b) 1600 (c) 1607
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is 48²? =
  30. 30.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 35² and 36²?
  32. 32.What is √841? =
  33. 33.Which of these is a perfect square? (a) 100 (b) 106 (c) 101
  34. 34.How many whole numbers lie between 30² and 31²?
  35. 35.How many whole numbers lie between 22² and 23²?
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  37. 37.A square garden has an area of 3600 square m. How long is each side (in m)?
  38. 38.A square garden has an area of 961 square m. How long is each side (in m)?
  39. 39.What is 35²? =
  40. 40.A square garden has an area of 36 square m. How long is each side (in m)?

Answer key

  1. 48
  2. 54
  3. 10
  4. 39
  5. 289
  6. 5
  7. 196
  8. 90
  9. 34
  10. 96
  11. 7569
  12. 9
  13. 1444
  14. 289
  15. 784
  16. 24
  17. 1296
  18. 52
  19. 53
  20. 225
  21. 17
  22. 12
  23. 225
  24. 3481
  25. 11
  26. 5
  27. 1600
  28. 676
  29. 2304
  30. 3
  31. 70
  32. 29
  33. 100
  34. 60
  35. 44
  36. 100
  37. 60
  38. 31
  39. 1225
  40. 6

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