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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 485 · 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 208 must be multiplied to get a perfect square?
  2. 2.What is the smallest whole number by which 56 must be divided to get a perfect square?
  3. 3.What is √1369? =
  4. 4.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √2916? =
  6. 6.What is √2500? =
  7. 7.What is 40²? =
  8. 8.Which of these is a perfect square? (a) 109 (b) 117 (c) 100
  9. 9.A square garden has an area of 729 square m. How long is each side (in m)?
  10. 10.What is 51²? =
  11. 11.What is √400? =
  12. 12.What is 65²? =
  13. 13.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 1336 (b) 1296 (c) 1306
  15. 15.What is √7056? =
  16. 16.A square garden has an area of 100 square m. How long is each side (in m)?
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is √441? =
  19. 19.What is √3481? =
  20. 20.What is √7569? =
  21. 21.What is 84²? =
  22. 22.Which of these is a perfect square? (a) 206 (b) 205 (c) 196
  23. 23.What is √1089? =
  24. 24.What is √361? =
  25. 25.A square garden has an area of 900 square m. How long is each side (in m)?
  26. 26.What is √3136? =
  27. 27.How many whole numbers lie between 43² and 44²?
  28. 28.What is √196? =
  29. 29.A square garden has an area of 400 square m. How long is each side (in m)?
  30. 30.How many whole numbers lie between 46² and 47²?
  31. 31.A square garden has an area of 169 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 8² and 9²?
  33. 33.How many whole numbers lie between 18² and 19²?
  34. 34.How many whole numbers lie between 32² and 33²?
  35. 35.How many whole numbers lie between 13² and 14²?
  36. 36.What is the smallest whole number by which 216 must be divided to get a perfect square?
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  39. 39.A square garden has an area of 1444 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 192 must be multiplied to get a perfect square?

Answer key

  1. 13
  2. 14
  3. 37
  4. 841
  5. 54
  6. 50
  7. 1600
  8. 100
  9. 27
  10. 2601
  11. 20
  12. 4225
  13. 14
  14. 1296
  15. 84
  16. 10
  17. 100
  18. 21
  19. 59
  20. 87
  21. 7056
  22. 196
  23. 33
  24. 19
  25. 30
  26. 56
  27. 86
  28. 14
  29. 20
  30. 92
  31. 13
  32. 16
  33. 36
  34. 64
  35. 26
  36. 6
  37. 324
  38. 64
  39. 38
  40. 3

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