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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 29 · 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 smallest whole number by which 45 must be divided to get a perfect square?
  2. 2.What is 48²? =
  3. 3.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √7225? =
  6. 6.What is the smallest whole number by which 125 must be divided to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 529 (b) 532 (c) 546
  8. 8.Which of these is a perfect square? (a) 246 (b) 225 (c) 237
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  10. 10.A square garden has an area of 256 square m. How long is each side (in m)?
  11. 11.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  12. 12.What is √361? =
  13. 13.Which of these is a perfect square? (a) 181 (b) 173 (c) 169
  14. 14.How many whole numbers lie between 13² and 14²?
  15. 15.What is 61²? =
  16. 16.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 839 (b) 784 (c) 823
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 29²? =
  20. 20.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 208 (b) 214 (c) 196
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 21²? =
  25. 25.How many whole numbers lie between 40² and 41²?
  26. 26.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  27. 27.A square garden has an area of 121 square m. How long is each side (in m)?
  28. 28.A square garden has an area of 289 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 49 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  32. 32.How many whole numbers lie between 18² and 19²?
  33. 33.How many whole numbers lie between 35² and 36²?
  34. 34.How many whole numbers lie between 50² and 51²?
  35. 35.What is √484? =
  36. 36.Which of these is a perfect square? (a) 592 (b) 576 (c) 586
  37. 37.What is 94²? =
  38. 38.How many whole numbers lie between 26² and 27²?
  39. 39.Which of these is a perfect square? (a) 146 (b) 162 (c) 144
  40. 40.What is the smallest whole number by which 396 must be divided to get a perfect square?

Answer key

  1. 5
  2. 2304
  3. 121
  4. 400
  5. 85
  6. 5
  7. 529
  8. 225
  9. 784
  10. 16
  11. 10
  12. 19
  13. 169
  14. 26
  15. 3721
  16. 11
  17. 784
  18. 225
  19. 841
  20. 15
  21. 14
  22. 196
  23. 900
  24. 441
  25. 80
  26. 15
  27. 11
  28. 17
  29. 196
  30. 7
  31. 841
  32. 36
  33. 70
  34. 100
  35. 22
  36. 576
  37. 8836
  38. 52
  39. 144
  40. 11

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