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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 483 · 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 48 must be divided to get a perfect square?
  2. 2.A square garden has an area of 2704 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 5² and 6²?
  6. 6.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  7. 7.What is 69²? =
  8. 8.Which of these is a perfect square? (a) 709 (b) 696 (c) 676
  9. 9.What is √625? =
  10. 10.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  11. 11.Which of these is a perfect square? (a) 193 (b) 184 (c) 169
  12. 12.What is the smallest whole number by which 90 must be divided to get a perfect square?
  13. 13.What is the smallest whole number by which 147 must be divided to get a perfect square?
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 8² and 9²?
  16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  17. 17.Which of these is a perfect square? (a) 577 (b) 605 (c) 576
  18. 18.What is √1225? =
  19. 19.What is √3136? =
  20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is √900? =
  22. 22.What is 35²? =
  23. 23.A square garden has an area of 256 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 2500 square m. How long is each side (in m)?
  25. 25.How many whole numbers lie between 19² and 20²?
  26. 26.What is √961? =
  27. 27.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  28. 28.How many whole numbers lie between 12² and 13²?
  29. 29.What is the smallest whole number by which 810 must be divided to get a perfect square?
  30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 32²? =
  33. 33.What is √676? =
  34. 34.Which of these is a perfect square? (a) 128 (b) 121 (c) 132
  35. 35.A square garden has an area of 961 square m. How long is each side (in m)?
  36. 36.A square garden has an area of 2916 square m. How long is each side (in m)?
  37. 37.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  38. 38.How many whole numbers lie between 33² and 34²?
  39. 39.What is √256? =
  40. 40.How many whole numbers lie between 9² and 10²?

Answer key

  1. 3
  2. 52
  3. 576
  4. 400
  5. 10
  6. 5
  7. 4761
  8. 676
  9. 25
  10. 14
  11. 169
  12. 10
  13. 3
  14. 784
  15. 16
  16. 676
  17. 576
  18. 35
  19. 56
  20. 900
  21. 30
  22. 1225
  23. 16
  24. 50
  25. 38
  26. 31
  27. 5
  28. 24
  29. 10
  30. 289
  31. 49
  32. 1024
  33. 26
  34. 121
  35. 31
  36. 54
  37. 5
  38. 66
  39. 16
  40. 18

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