← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 14 · 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 540 must be multiplied to get a perfect square?
  2. 2.What is the smallest whole number by which 63 must be divided to get a perfect square?
  3. 3.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 100 (b) 119 (c) 118
  6. 6.What is √961? =
  7. 7.Which of these is a perfect square? (a) 961 (b) 967 (c) 1018
  8. 8.What is √3364? =
  9. 9.Which of these is a perfect square? (a) 721 (b) 709 (c) 676
  10. 10.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 463 (b) 441 (c) 471
  12. 12.What is the smallest whole number by which 98 must be divided to get a perfect square?
  13. 13.How many whole numbers lie between 13² and 14²?
  14. 14.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  15. 15.What is 34²? =
  16. 16.What is √6561? =
  17. 17.How many whole numbers lie between 17² and 18²?
  18. 18.A square garden has an area of 529 square m. How long is each side (in m)?
  19. 19.How many whole numbers lie between 21² and 22²?
  20. 20.What is 41²? =
  21. 21.What is √7569? =
  22. 22.What is 73²? =
  23. 23.What is √729? =
  24. 24.What is 26²? =
  25. 25.Which of these is a perfect square? (a) 1218 (b) 1156 (c) 1169
  26. 26.What is √3969? =
  27. 27.What is √9025? =
  28. 28.How many whole numbers lie between 25² and 26²?
  29. 29.A square garden has an area of 256 square m. How long is each side (in m)?
  30. 30.What is √900? =
  31. 31.What is 60²? =
  32. 32.What is 65²? =
  33. 33.What is √1296? =
  34. 34.What is √3600? =
  35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is √289? =
  37. 37.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 78²? =
  40. 40.How many whole numbers lie between 10² and 11²?

Answer key

  1. 15
  2. 7
  3. 3
  4. 784
  5. 100
  6. 31
  7. 961
  8. 58
  9. 676
  10. 5
  11. 441
  12. 2
  13. 26
  14. 6
  15. 1156
  16. 81
  17. 34
  18. 23
  19. 42
  20. 1681
  21. 87
  22. 5329
  23. 27
  24. 676
  25. 1156
  26. 63
  27. 95
  28. 50
  29. 16
  30. 30
  31. 3600
  32. 4225
  33. 36
  34. 60
  35. 256
  36. 17
  37. 625
  38. 400
  39. 6084
  40. 20

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