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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 444 · 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 36² and 37²?
  2. 2.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 1011 (b) 961 (c) 963
  4. 4.What is √5476? =
  5. 5.What is 93²? =
  6. 6.A square garden has an area of 576 square m. How long is each side (in m)?
  7. 7.What is √6889? =
  8. 8.A square garden has an area of 225 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 21² and 22²?
  10. 10.Which of these is a perfect square? (a) 187 (b) 189 (c) 169
  11. 11.How many whole numbers lie between 18² and 19²?
  12. 12.What is 89²? =
  13. 13.Which of these is a perfect square? (a) 128 (b) 121 (c) 125
  14. 14.Which of these is a perfect square? (a) 428 (b) 400 (c) 426
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  16. 16.A square garden has an area of 2704 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  19. 19.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  20. 20.What is 33²? =
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 37²? =
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 1225 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  27. 27.How many whole numbers lie between 39² and 40²?
  28. 28.How many whole numbers lie between 17² and 18²?
  29. 29.What is 79²? =
  30. 30.Which of these is a perfect square? (a) 1285 (b) 1239 (c) 1225
  31. 31.A square garden has an area of 1521 square m. How long is each side (in m)?
  32. 32.What is 44²? =
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  34. 34.Which of these is a perfect square? (a) 734 (b) 729 (c) 771
  35. 35.Which of these is a perfect square? (a) 915 (b) 900 (c) 911
  36. 36.What is the smallest whole number by which 486 must be divided to get a perfect square?
  37. 37.What is √484? =
  38. 38.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √5041? =
  40. 40.Which of these is a perfect square? (a) 1658 (b) 1611 (c) 1600

Answer key

  1. 72
  2. 14
  3. 961
  4. 74
  5. 8649
  6. 24
  7. 83
  8. 15
  9. 42
  10. 169
  11. 36
  12. 7921
  13. 121
  14. 400
  15. 400
  16. 52
  17. 64
  18. 3
  19. 2
  20. 1089
  21. 25
  22. 1369
  23. 784
  24. 35
  25. 324
  26. 225
  27. 78
  28. 34
  29. 6241
  30. 1225
  31. 39
  32. 1936
  33. 625
  34. 729
  35. 900
  36. 6
  37. 22
  38. 529
  39. 71
  40. 1600

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