← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 706 · 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 49²? =
  2. 2.What is the smallest whole number by which 325 must be divided to get a perfect square?
  3. 3.What is √4761? =
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 125 must be divided to get a perfect square?
  6. 6.What is √289? =
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.A square garden has an area of 2116 square m. How long is each side (in m)?
  9. 9.A square garden has an area of 225 square m. How long is each side (in m)?
  10. 10.A square garden has an area of 361 square m. How long is each side (in m)?
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 8 must be divided to get a perfect square?
  13. 13.What is 67²? =
  14. 14.A square garden has an area of 2500 square m. How long is each side (in m)?
  15. 15.What is √5184? =
  16. 16.What is 69²? =
  17. 17.What is 44²? =
  18. 18.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 637 must be divided to get a perfect square?
  20. 20.What is √6561? =
  21. 21.What is 81²? =
  22. 22.A square garden has an area of 169 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 16² and 17²?
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is the smallest whole number by which 896 must be divided to get a perfect square?
  26. 26.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 3481 square m. How long is each side (in m)?
  28. 28.How many whole numbers lie between 41² and 42²?
  29. 29.A square garden has an area of 400 square m. How long is each side (in m)?
  30. 30.What is √3600? =
  31. 31.What is √2704? =
  32. 32.How many whole numbers lie between 40² and 41²?
  33. 33.How many whole numbers lie between 35² and 36²?
  34. 34.What is 21²? =
  35. 35.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  36. 36.What is √676? =
  37. 37.How many whole numbers lie between 44² and 45²?
  38. 38.What is √1024? =
  39. 39.A square garden has an area of 1521 square m. How long is each side (in m)?
  40. 40.Which of these is a perfect square? (a) 151 (b) 157 (c) 144

Answer key

  1. 2401
  2. 13
  3. 69
  4. 25
  5. 5
  6. 17
  7. 9
  8. 46
  9. 15
  10. 19
  11. 289
  12. 2
  13. 4489
  14. 50
  15. 72
  16. 4761
  17. 1936
  18. 5
  19. 13
  20. 81
  21. 6561
  22. 13
  23. 32
  24. 49
  25. 14
  26. 169
  27. 59
  28. 82
  29. 20
  30. 60
  31. 52
  32. 80
  33. 70
  34. 441
  35. 10
  36. 26
  37. 88
  38. 32
  39. 39
  40. 144

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