← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 32 · 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 √3600? =
  2. 2.How many whole numbers lie between 27² and 28²?
  3. 3.What is √1849? =
  4. 4.What is √961? =
  5. 5.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is 62²? =
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √9216? =
  9. 9.How many whole numbers lie between 45² and 46²?
  10. 10.What is √2601? =
  11. 11.What is 25²? =
  12. 12.How many whole numbers lie between 20² and 21²?
  13. 13.What is the smallest whole number by which 343 must be divided to get a perfect square?
  14. 14.What is √1225? =
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the smallest whole number by which 135 must be divided to get a perfect square?
  17. 17.What is √1296? =
  18. 18.Which of these is a perfect square? (a) 1225 (b) 1242 (c) 1262
  19. 19.What is 20²? =
  20. 20.What is 72²? =
  21. 21.A square garden has an area of 361 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  23. 23.What is the smallest whole number by which 490 must be divided to get a perfect square?
  24. 24.What is √144? =
  25. 25.What is the smallest whole number by which 12 must be divided to get a perfect square?
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √256? =
  28. 28.What is √6889? =
  29. 29.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  31. 31.A square garden has an area of 676 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 360 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
  34. 34.How many whole numbers lie between 43² and 44²?
  35. 35.Which of these is a perfect square? (a) 529 (b) 570 (c) 536
  36. 36.What is √625? =
  37. 37.Which of these is a perfect square? (a) 144 (b) 155 (c) 153
  38. 38.What is 14²? =
  39. 39.What is √1444? =
  40. 40.What is 28²? =

Answer key

  1. 60
  2. 54
  3. 43
  4. 31
  5. 484
  6. 3844
  7. 256
  8. 96
  9. 90
  10. 51
  11. 625
  12. 40
  13. 7
  14. 35
  15. 400
  16. 15
  17. 36
  18. 1225
  19. 400
  20. 5184
  21. 19
  22. 6
  23. 10
  24. 12
  25. 3
  26. 625
  27. 16
  28. 83
  29. 676
  30. 6
  31. 26
  32. 10
  33. 13
  34. 86
  35. 529
  36. 25
  37. 144
  38. 196
  39. 38
  40. 784

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