← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 352 · 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 117 must be multiplied to get a perfect square?
  2. 2.How many whole numbers lie between 17² and 18²?
  3. 3.What is √4489? =
  4. 4.Which of these is a perfect square? (a) 275 (b) 260 (c) 256
  5. 5.How many whole numbers lie between 34² and 35²?
  6. 6.What is the smallest whole number by which 294 must be divided to get a perfect square?
  7. 7.A square garden has an area of 324 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 2704 square m. How long is each side (in m)?
  9. 9.What is √6889? =
  10. 10.A square garden has an area of 2500 square m. How long is each side (in m)?
  11. 11.What is 50²? =
  12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 18² and 19²?
  14. 14.A square garden has an area of 1024 square m. How long is each side (in m)?
  15. 15.What is √2500? =
  16. 16.A square garden has an area of 729 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 183 (b) 169 (c) 171
  18. 18.Which of these is a perfect square? (a) 317 (b) 290 (c) 289
  19. 19.What is 32²? =
  20. 20.What is 99²? =
  21. 21.Which of these is a perfect square? (a) 223 (b) 224 (c) 196
  22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √400? =
  24. 24.What is 54²? =
  25. 25.Which of these is a perfect square? (a) 671 (b) 652 (c) 625
  26. 26.A square garden has an area of 1600 square m. How long is each side (in m)?
  27. 27.What is √1089? =
  28. 28.Which of these is a perfect square? (a) 529 (b) 562 (c) 537
  29. 29.Which of these is a perfect square? (a) 340 (b) 324 (c) 352
  30. 30.A square garden has an area of 841 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 1461 (b) 1444 (c) 1464
  33. 33.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  34. 34.How many whole numbers lie between 14² and 15²?
  35. 35.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  36. 36.What is √2401? =
  37. 37.What is the smallest whole number by which 72 must be divided to get a perfect square?
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 2601 square m. How long is each side (in m)?
  40. 40.What is 67²? =

Answer key

  1. 13
  2. 34
  3. 67
  4. 256
  5. 68
  6. 6
  7. 18
  8. 52
  9. 83
  10. 50
  11. 2500
  12. 484
  13. 36
  14. 32
  15. 50
  16. 27
  17. 169
  18. 289
  19. 1024
  20. 9801
  21. 196
  22. 324
  23. 20
  24. 2916
  25. 625
  26. 40
  27. 33
  28. 529
  29. 324
  30. 29
  31. 25
  32. 1444
  33. 14
  34. 28
  35. 5
  36. 49
  37. 2
  38. 36
  39. 51
  40. 4489

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