← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 587 · 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 sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 25 square m. How long is each side (in m)?
  3. 3.What is 36²? =
  4. 4.What is √2704? =
  5. 5.What is 79²? =
  6. 6.What is √3025? =
  7. 7.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 19² and 20²?
  10. 10.Which of these is a perfect square? (a) 1296 (b) 1354 (c) 1341
  11. 11.How many whole numbers lie between 50² and 51²?
  12. 12.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  13. 13.What is √9604? =
  14. 14.What is 22²? =
  15. 15.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  16. 16.A square garden has an area of 441 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 686 (b) 715 (c) 676
  18. 18.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
  19. 19.What is 28²? =
  20. 20.Which of these is a perfect square? (a) 1622 (b) 1600 (c) 1657
  21. 21.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  22. 22.A square garden has an area of 1936 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 41² and 42²?
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  25. 25.A square garden has an area of 1444 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  28. 28.A square garden has an area of 289 square m. How long is each side (in m)?
  29. 29.Which of these is a perfect square? (a) 453 (b) 441 (c) 469
  30. 30.What is 11²? =
  31. 31.How many whole numbers lie between 21² and 22²?
  32. 32.What is 64²? =
  33. 33.What is 49²? =
  34. 34.What is √3364? =
  35. 35.A square garden has an area of 3364 square m. How long is each side (in m)?
  36. 36.What is 55²? =
  37. 37.What is 59²? =
  38. 38.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 1156 (b) 1165 (c) 1196
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 676
  2. 5
  3. 1296
  4. 52
  5. 6241
  6. 55
  7. 196
  8. 36
  9. 38
  10. 1296
  11. 100
  12. 11
  13. 98
  14. 484
  15. 7
  16. 21
  17. 676
  18. 5
  19. 784
  20. 1600
  21. 5
  22. 44
  23. 82
  24. 256
  25. 38
  26. 86
  27. 3
  28. 17
  29. 441
  30. 121
  31. 42
  32. 4096
  33. 2401
  34. 58
  35. 58
  36. 3025
  37. 3481
  38. 7
  39. 1156
  40. 100

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