← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 433 · 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.Which of these is a perfect square? (a) 307 (b) 289 (c) 316
  2. 2.What is the smallest whole number by which 250 must be divided to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 257 (b) 278 (c) 256
  4. 4.A square garden has an area of 576 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 36² and 37²?
  8. 8.A square garden has an area of 1089 square m. How long is each side (in m)?
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 1376 (b) 1369 (c) 1382
  11. 11.A square garden has an area of 1156 square m. How long is each side (in m)?
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 35² and 36²?
  15. 15.What is √9604? =
  16. 16.What is 40²? =
  17. 17.What is √289? =
  18. 18.How many whole numbers lie between 31² and 32²?
  19. 19.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  20. 20.How many whole numbers lie between 14² and 15²?
  21. 21.What is √1225? =
  22. 22.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 25 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 49² and 50²?
  26. 26.A square garden has an area of 1444 square m. How long is each side (in m)?
  27. 27.What is √5625? =
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √1296? =
  30. 30.How many whole numbers lie between 46² and 47²?
  31. 31.Which of these is a perfect square? (a) 324 (b) 349 (c) 342
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  33. 33.A square garden has an area of 64 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 6² and 7²?
  35. 35.A square garden has an area of 3249 square m. How long is each side (in m)?
  36. 36.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 192 must be divided to get a perfect square?
  38. 38.What is the smallest whole number by which 48 must be divided to get a perfect square?
  39. 39.What is 15²? =
  40. 40.What is 47²? =

Answer key

  1. 289
  2. 10
  3. 256
  4. 24
  5. 10
  6. 144
  7. 72
  8. 33
  9. 121
  10. 1369
  11. 34
  12. 169
  13. 441
  14. 70
  15. 98
  16. 1600
  17. 17
  18. 62
  19. 529
  20. 28
  21. 35
  22. 676
  23. 2
  24. 5
  25. 98
  26. 38
  27. 75
  28. 841
  29. 36
  30. 92
  31. 324
  32. 324
  33. 8
  34. 12
  35. 57
  36. 784
  37. 3
  38. 3
  39. 225
  40. 2209

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