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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 136 · 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 32 must be divided to get a perfect square?
  2. 2.What is √1369? =
  3. 3.What is 19²? =
  4. 4.What is the smallest whole number by which 8 must be divided to get a perfect square?
  5. 5.What is √1296? =
  6. 6.What is √7921? =
  7. 7.How many whole numbers lie between 40² and 41²?
  8. 8.What is √196? =
  9. 9.Which of these is a perfect square? (a) 289 (b) 318 (c) 317
  10. 10.What is 86²? =
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  13. 13.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 6² and 7²?
  15. 15.Which of these is a perfect square? (a) 537 (b) 567 (c) 529
  16. 16.How many whole numbers lie between 7² and 8²?
  17. 17.How many whole numbers lie between 41² and 42²?
  18. 18.What is √2809? =
  19. 19.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 2401 square m. How long is each side (in m)?
  21. 21.What is 21²? =
  22. 22.A square garden has an area of 64 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 17² and 18²?
  24. 24.Which of these is a perfect square? (a) 576 (b) 619 (c) 587
  25. 25.What is 24²? =
  26. 26.Which of these is a perfect square? (a) 165 (b) 144 (c) 155
  27. 27.What is √3481? =
  28. 28.Which of these is a perfect square? (a) 324 (b) 355 (c) 354
  29. 29.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  30. 30.A square garden has an area of 36 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 324 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 44² and 45²?
  33. 33.A square garden has an area of 169 square m. How long is each side (in m)?
  34. 34.A square garden has an area of 784 square m. How long is each side (in m)?
  35. 35.What is √4900? =
  36. 36.How many whole numbers lie between 15² and 16²?
  37. 37.A square garden has an area of 676 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
  39. 39.What is 47²? =
  40. 40.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 2
  2. 37
  3. 361
  4. 2
  5. 36
  6. 89
  7. 80
  8. 14
  9. 289
  10. 7396
  11. 289
  12. 3
  13. 11
  14. 12
  15. 529
  16. 14
  17. 82
  18. 53
  19. 3
  20. 49
  21. 441
  22. 8
  23. 34
  24. 576
  25. 576
  26. 144
  27. 59
  28. 324
  29. 49
  30. 6
  31. 18
  32. 88
  33. 13
  34. 28
  35. 70
  36. 30
  37. 26
  38. 13
  39. 2209
  40. 900

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