← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 700 · 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.Which of these is a perfect square? (a) 1089 (b) 1105 (c) 1151
  2. 2.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 46²? =
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
  7. 7.What is the smallest whole number by which 117 must be divided to get a perfect square?
  8. 8.A square garden has an area of 225 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 256 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 176 must be divided to get a perfect square?
  13. 13.What is 72²? =
  14. 14.A square garden has an area of 2500 square m. How long is each side (in m)?
  15. 15.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 32²? =
  18. 18.What is 61²? =
  19. 19.What is √8836? =
  20. 20.What is √3721? =
  21. 21.What is √3025? =
  22. 22.Which of these is a perfect square? (a) 1299 (b) 1312 (c) 1296
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  25. 25.How many whole numbers lie between 10² and 11²?
  26. 26.A square garden has an area of 144 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 50² and 51²?
  28. 28.How many whole numbers lie between 23² and 24²?
  29. 29.What is √6084? =
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 504 must be divided to get a perfect square?
  32. 32.What is 26²? =
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 529 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 452 (b) 478 (c) 441
  36. 36.What is √2809? =
  37. 37.What is √6400? =
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.How many whole numbers lie between 16² and 17²?
  40. 40.What is 20²? =

Answer key

  1. 1089
  2. 5
  3. 400
  4. 2116
  5. 100
  6. 2
  7. 13
  8. 15
  9. 289
  10. 16
  11. 196
  12. 11
  13. 5184
  14. 50
  15. 14
  16. 169
  17. 1024
  18. 3721
  19. 94
  20. 61
  21. 55
  22. 1296
  23. 324
  24. 5
  25. 20
  26. 12
  27. 100
  28. 46
  29. 78
  30. 36
  31. 14
  32. 676
  33. 361
  34. 23
  35. 441
  36. 53
  37. 80
  38. 54
  39. 32
  40. 400

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