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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 605 · 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 58²? =
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √4096? =
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 176 (b) 169 (c) 185
  6. 6.A square garden has an area of 2025 square m. How long is each side (in m)?
  7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 90²? =
  9. 9.What is 20²? =
  10. 10.What is 30²? =
  11. 11.What is 32²? =
  12. 12.What is √196? =
  13. 13.How many whole numbers lie between 13² and 14²?
  14. 14.Which of these is a perfect square? (a) 841 (b) 848 (c) 845
  15. 15.What is the smallest whole number by which 384 must be divided to get a perfect square?
  16. 16.What is 87²? =
  17. 17.What is √1681? =
  18. 18.What is 79²? =
  19. 19.What is √169? =
  20. 20.A square garden has an area of 1681 square m. How long is each side (in m)?
  21. 21.What is √3721? =
  22. 22.How many whole numbers lie between 10² and 11²?
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 3136 square m. How long is each side (in m)?
  25. 25.A square garden has an area of 1156 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 8² and 9²?
  27. 27.What is √324? =
  28. 28.What is the smallest whole number by which 48 must be divided to get a perfect square?
  29. 29.What is 60²? =
  30. 30.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 16² and 17²?
  32. 32.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  33. 33.A square garden has an area of 196 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 7² and 8²?
  35. 35.What is 89²? =
  36. 36.A square garden has an area of 256 square m. How long is each side (in m)?
  37. 37.What is 28²? =
  38. 38.Which of these is a perfect square? (a) 961 (b) 978 (c) 1002
  39. 39.What is √9801? =
  40. 40.Which of these is a perfect square? (a) 1347 (b) 1352 (c) 1296

Answer key

  1. 3364
  2. 25
  3. 64
  4. 900
  5. 169
  6. 45
  7. 225
  8. 8100
  9. 400
  10. 900
  11. 1024
  12. 14
  13. 26
  14. 841
  15. 6
  16. 7569
  17. 41
  18. 6241
  19. 13
  20. 41
  21. 61
  22. 20
  23. 361
  24. 56
  25. 34
  26. 16
  27. 18
  28. 3
  29. 3600
  30. 11
  31. 32
  32. 15
  33. 14
  34. 14
  35. 7921
  36. 16
  37. 784
  38. 961
  39. 99
  40. 1296

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