← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 260 · 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 √289? =
  2. 2.What is √3136? =
  3. 3.How many whole numbers lie between 24² and 25²?
  4. 4.What is the smallest whole number by which 8 must be divided to get a perfect square?
  5. 5.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  6. 6.A square garden has an area of 169 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 6² and 7²?
  10. 10.What is √7569? =
  11. 11.How many whole numbers lie between 32² and 33²?
  12. 12.Which of these is a perfect square? (a) 820 (b) 784 (c) 796
  13. 13.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 27² and 28²?
  15. 15.Which of these is a perfect square? (a) 1296 (b) 1301 (c) 1317
  16. 16.Which of these is a perfect square? (a) 466 (b) 441 (c) 459
  17. 17.How many whole numbers lie between 39² and 40²?
  18. 18.What is √4096? =
  19. 19.How many whole numbers lie between 22² and 23²?
  20. 20.Which of these is a perfect square? (a) 405 (b) 407 (c) 400
  21. 21.A square garden has an area of 441 square m. How long is each side (in m)?
  22. 22.A square garden has an area of 1369 square m. How long is each side (in m)?
  23. 23.What is 90²? =
  24. 24.Which of these is a perfect square? (a) 364 (b) 392 (c) 361
  25. 25.Which of these is a perfect square? (a) 518 (b) 484 (c) 490
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 31²? =
  29. 29.How many whole numbers lie between 12² and 13²?
  30. 30.A square garden has an area of 1681 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  32. 32.Which of these is a perfect square? (a) 1270 (b) 1249 (c) 1225
  33. 33.Which of these is a perfect square? (a) 1024 (b) 1025 (c) 1034
  34. 34.What is 19²? =
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 541 (b) 529 (c) 530
  37. 37.A square garden has an area of 900 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 11² and 12²?
  39. 39.Which of these is a perfect square? (a) 108 (b) 100 (c) 105
  40. 40.What is 28²? =

Answer key

  1. 17
  2. 56
  3. 48
  4. 2
  5. 3
  6. 13
  7. 9
  8. 49
  9. 12
  10. 87
  11. 64
  12. 784
  13. 5
  14. 54
  15. 1296
  16. 441
  17. 78
  18. 64
  19. 44
  20. 400
  21. 21
  22. 37
  23. 8100
  24. 361
  25. 484
  26. 121
  27. 64
  28. 961
  29. 24
  30. 41
  31. 14
  32. 1225
  33. 1024
  34. 361
  35. 25
  36. 529
  37. 30
  38. 22
  39. 100
  40. 784

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