← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 603 · 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 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 225 square m. How long is each side (in m)?
  3. 3.How many whole numbers lie between 18² and 19²?
  4. 4.What is the smallest whole number by which 96 must be divided to get a perfect square?
  5. 5.What is 15²? =
  6. 6.How many whole numbers lie between 13² and 14²?
  7. 7.Which of these is a perfect square? (a) 872 (b) 843 (c) 841
  8. 8.Which of these is a perfect square? (a) 794 (b) 784 (c) 814
  9. 9.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  10. 10.How many whole numbers lie between 30² and 31²?
  11. 11.A square garden has an area of 2304 square m. How long is each side (in m)?
  12. 12.What is 25²? =
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the smallest whole number by which 504 must be divided to get a perfect square?
  15. 15.Which of these is a perfect square? (a) 256 (b) 259 (c) 267
  16. 16.What is √784? =
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √2500? =
  19. 19.What is √2116? =
  20. 20.What is √1296? =
  21. 21.What is √1225? =
  22. 22.A square garden has an area of 2601 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 627 (b) 625 (c) 662
  26. 26.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is √484? =
  28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 900 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 35² and 36²?
  31. 31.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  33. 33.How many whole numbers lie between 10² and 11²?
  34. 34.What is 28²? =
  35. 35.What is √3136? =
  36. 36.A square garden has an area of 1156 square m. How long is each side (in m)?
  37. 37.Which of these is a perfect square? (a) 1397 (b) 1369 (c) 1385
  38. 38.What is 42²? =
  39. 39.What is 21²? =
  40. 40.What is the smallest whole number by which 75 must be multiplied to get a perfect square?

Answer key

  1. 36
  2. 15
  3. 36
  4. 6
  5. 225
  6. 26
  7. 841
  8. 784
  9. 3
  10. 60
  11. 48
  12. 625
  13. 144
  14. 14
  15. 256
  16. 28
  17. 289
  18. 50
  19. 46
  20. 36
  21. 35
  22. 51
  23. 196
  24. 7
  25. 625
  26. 729
  27. 22
  28. 484
  29. 30
  30. 70
  31. 100
  32. 11
  33. 20
  34. 784
  35. 56
  36. 34
  37. 1369
  38. 1764
  39. 441
  40. 3

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