← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 129 · 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.A square garden has an area of 196 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 24 must be divided to get a perfect square?
  3. 3.What is √7396? =
  4. 4.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 22² and 23²?
  6. 6.Which of these is a perfect square? (a) 229 (b) 225 (c) 234
  7. 7.A square garden has an area of 1936 square m. How long is each side (in m)?
  8. 8.What is 91²? =
  9. 9.Which of these is a perfect square? (a) 1296 (b) 1314 (c) 1348
  10. 10.Which of these is a perfect square? (a) 727 (b) 700 (c) 676
  11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 12² and 13²?
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is √3364? =
  15. 15.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  16. 16.A square garden has an area of 1600 square m. How long is each side (in m)?
  17. 17.A square garden has an area of 3025 square m. How long is each side (in m)?
  18. 18.How many whole numbers lie between 8² and 9²?
  19. 19.How many whole numbers lie between 19² and 20²?
  20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
  21. 21.What is 13²? =
  22. 22.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 1232 (b) 1262 (c) 1225
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √196? =
  26. 26.What is √3600? =
  27. 27.Which of these is a perfect square? (a) 1403 (b) 1424 (c) 1369
  28. 28.What is √4225? =
  29. 29.What is 58²? =
  30. 30.What is 65²? =
  31. 31.What is 26²? =
  32. 32.How many whole numbers lie between 37² and 38²?
  33. 33.What is √7569? =
  34. 34.What is √1600? =
  35. 35.How many whole numbers lie between 24² and 25²?
  36. 36.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 109 (b) 119 (c) 100
  39. 39.How many whole numbers lie between 11² and 12²?
  40. 40.What is 60²? =

Answer key

  1. 14
  2. 6
  3. 86
  4. 5
  5. 44
  6. 225
  7. 44
  8. 8281
  9. 1296
  10. 676
  11. 324
  12. 24
  13. 49
  14. 58
  15. 10
  16. 40
  17. 55
  18. 16
  19. 38
  20. 20
  21. 169
  22. 5
  23. 1225
  24. 100
  25. 14
  26. 60
  27. 1369
  28. 65
  29. 3364
  30. 4225
  31. 676
  32. 74
  33. 87
  34. 40
  35. 48
  36. 10
  37. 121
  38. 100
  39. 22
  40. 3600

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