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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 350 · 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.How many whole numbers lie between 17² and 18²?
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
  5. 5.What is √5776? =
  6. 6.A square garden has an area of 3364 square m. How long is each side (in m)?
  7. 7.What is the smallest whole number by which 52 must be divided to get a perfect square?
  8. 8.What is √4096? =
  9. 9.How many whole numbers lie between 10² and 11²?
  10. 10.Which of these is a perfect square? (a) 576 (b) 619 (c) 580
  11. 11.A square garden has an area of 1156 square m. How long is each side (in m)?
  12. 12.What is 94²? =
  13. 13.How many whole numbers lie between 5² and 6²?
  14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  15. 15.A square garden has an area of 144 square m. How long is each side (in m)?
  16. 16.What is √196? =
  17. 17.What is the smallest whole number by which 128 must be divided to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 441 (b) 446 (c) 449
  19. 19.What is 38²? =
  20. 20.What is the smallest whole number by which 468 must be divided to get a perfect square?
  21. 21.What is 12²? =
  22. 22.Which of these is a perfect square? (a) 152 (b) 158 (c) 144
  23. 23.How many whole numbers lie between 43² and 44²?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.What is √3364? =
  26. 26.What is √625? =
  27. 27.How many whole numbers lie between 36² and 37²?
  28. 28.How many whole numbers lie between 13² and 14²?
  29. 29.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 240 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 529 (b) 552 (c) 554
  32. 32.What is 53²? =
  33. 33.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 26² and 27²?
  36. 36.What is the smallest whole number by which 117 must be divided to get a perfect square?
  37. 37.What is the smallest whole number by which 80 must be divided to get a perfect square?
  38. 38.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  39. 39.What is √400? =
  40. 40.What is √1296? =

Answer key

  1. 34
  2. 121
  3. 484
  4. 6
  5. 76
  6. 58
  7. 13
  8. 64
  9. 20
  10. 576
  11. 34
  12. 8836
  13. 10
  14. 169
  15. 12
  16. 14
  17. 2
  18. 441
  19. 1444
  20. 13
  21. 144
  22. 144
  23. 86
  24. 64
  25. 58
  26. 25
  27. 72
  28. 26
  29. 36
  30. 15
  31. 529
  32. 2809
  33. 676
  34. 41
  35. 52
  36. 13
  37. 5
  38. 2
  39. 20
  40. 36

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