← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 359 · 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 49 square m. How long is each side (in m)?
  2. 2.What is the smallest whole number by which 405 must be divided to get a perfect square?
  3. 3.What is the smallest whole number by which 810 must be divided to get a perfect square?
  4. 4.What is the smallest whole number by which 640 must be divided to get a perfect square?
  5. 5.What is 59²? =
  6. 6.What is √3969? =
  7. 7.What is √4624? =
  8. 8.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  10. 10.What is √2704? =
  11. 11.How many whole numbers lie between 40² and 41²?
  12. 12.A square garden has an area of 2116 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 1521 (b) 1599 (c) 1589
  14. 14.A square garden has an area of 1225 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 8² and 9²?
  16. 16.What is 22²? =
  17. 17.Which of these is a perfect square? (a) 144 (b) 153 (c) 147
  18. 18.A square garden has an area of 196 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 504 must be divided to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 786 (b) 820 (c) 784
  21. 21.What is 57²? =
  22. 22.What is √361? =
  23. 23.What is √8464? =
  24. 24.Which of these is a perfect square? (a) 1248 (b) 1239 (c) 1225
  25. 25.Which of these is a perfect square? (a) 1668 (b) 1633 (c) 1600
  26. 26.How many whole numbers lie between 48² and 49²?
  27. 27.What is √841? =
  28. 28.What is √961? =
  29. 29.What is the smallest whole number by which 48 must be divided to get a perfect square?
  30. 30.How many whole numbers lie between 43² and 44²?
  31. 31.What is √1024? =
  32. 32.What is the smallest whole number by which 490 must be divided to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 1168 (b) 1156 (c) 1175
  34. 34.A square garden has an area of 784 square m. How long is each side (in m)?
  35. 35.What is 58²? =
  36. 36.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  37. 37.Which of these is a perfect square? (a) 469 (b) 461 (c) 441
  38. 38.What is the smallest whole number by which 252 must be divided to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 400 (b) 407 (c) 405
  40. 40.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 7
  2. 5
  3. 10
  4. 10
  5. 3481
  6. 63
  7. 68
  8. 6
  9. 2
  10. 52
  11. 80
  12. 46
  13. 1521
  14. 35
  15. 16
  16. 484
  17. 144
  18. 14
  19. 14
  20. 784
  21. 3249
  22. 19
  23. 92
  24. 1225
  25. 1600
  26. 96
  27. 29
  28. 31
  29. 3
  30. 86
  31. 32
  32. 10
  33. 1156
  34. 28
  35. 3364
  36. 15
  37. 441
  38. 7
  39. 400
  40. 841

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