← Squares and square roots lesson New set →

Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 205 · 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) 1384 (b) 1412 (c) 1369
  2. 2.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  3. 3.A square garden has an area of 324 square m. How long is each side (in m)?
  4. 4.What is the smallest whole number by which 245 must be divided to get a perfect square?
  5. 5.Which of these is a perfect square? (a) 484 (b) 518 (c) 519
  6. 6.Which of these is a perfect square? (a) 1195 (b) 1156 (c) 1186
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 17²? =
  9. 9.How many whole numbers lie between 20² and 21²?
  10. 10.How many whole numbers lie between 24² and 25²?
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 44² and 45²?
  13. 13.How many whole numbers lie between 31² and 32²?
  14. 14.What is √4489? =
  15. 15.A square garden has an area of 2116 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 5² and 6²?
  17. 17.Which of these is a perfect square? (a) 169 (b) 179 (c) 174
  18. 18.What is 40²? =
  19. 19.What is √9025? =
  20. 20.What is √2304? =
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 135 must be divided to get a perfect square?
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the smallest whole number by which 252 must be divided to get a perfect square?
  25. 25.A square garden has an area of 441 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 96 must be divided to get a perfect square?
  27. 27.A square garden has an area of 3025 square m. How long is each side (in m)?
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 2025 square m. How long is each side (in m)?
  31. 31.What is 48²? =
  32. 32.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
  33. 33.How many whole numbers lie between 50² and 51²?
  34. 34.How many whole numbers lie between 49² and 50²?
  35. 35.How many whole numbers lie between 11² and 12²?
  36. 36.Which of these is a perfect square? (a) 885 (b) 841 (c) 848
  37. 37.What is 56²? =
  38. 38.How many whole numbers lie between 6² and 7²?
  39. 39.What is 79²? =
  40. 40.Which of these is a perfect square? (a) 570 (b) 534 (c) 529

Answer key

  1. 1369
  2. 484
  3. 18
  4. 5
  5. 484
  6. 1156
  7. 529
  8. 289
  9. 40
  10. 48
  11. 121
  12. 88
  13. 62
  14. 67
  15. 46
  16. 10
  17. 169
  18. 1600
  19. 95
  20. 48
  21. 441
  22. 15
  23. 64
  24. 7
  25. 21
  26. 6
  27. 55
  28. 36
  29. 361
  30. 45
  31. 2304
  32. 7
  33. 100
  34. 98
  35. 22
  36. 841
  37. 3136
  38. 12
  39. 6241
  40. 529

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