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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 562 · 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 28² and 29²?
  2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  3. 3.How many whole numbers lie between 42² and 43²?
  4. 4.A square garden has an area of 144 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 121 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 265 (b) 278 (c) 256
  8. 8.What is √2500? =
  9. 9.A square garden has an area of 3136 square m. How long is each side (in m)?
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 1225 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 24² and 25²?
  13. 13.What is 79²? =
  14. 14.What is √1936? =
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  16. 16.How many whole numbers lie between 15² and 16²?
  17. 17.What is √7056? =
  18. 18.How many whole numbers lie between 44² and 45²?
  19. 19.Which of these is a perfect square? (a) 1519 (b) 1451 (c) 1444
  20. 20.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  21. 21.What is the smallest whole number by which 208 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1061 (b) 1041 (c) 1024
  23. 23.What is √1296? =
  24. 24.What is the smallest whole number by which 32 must be divided to get a perfect square?
  25. 25.A square garden has an area of 361 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 9² and 10²?
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  28. 28.How many whole numbers lie between 17² and 18²?
  29. 29.A square garden has an area of 2809 square m. How long is each side (in m)?
  30. 30.What is 44²? =
  31. 31.What is 70²? =
  32. 32.What is √6724? =
  33. 33.What is √529? =
  34. 34.Which of these is a perfect square? (a) 1575 (b) 1521 (c) 1594
  35. 35.What is 95²? =
  36. 36.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  37. 37.What is 42²? =
  38. 38.A square garden has an area of 256 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 100 (b) 118 (c) 106
  40. 40.A square garden has an area of 1156 square m. How long is each side (in m)?

Answer key

  1. 56
  2. 25
  3. 84
  4. 12
  5. 11
  6. 6
  7. 256
  8. 50
  9. 56
  10. 676
  11. 35
  12. 48
  13. 6241
  14. 44
  15. 100
  16. 30
  17. 84
  18. 88
  19. 1444
  20. 2
  21. 13
  22. 1024
  23. 36
  24. 2
  25. 19
  26. 18
  27. 484
  28. 34
  29. 53
  30. 1936
  31. 4900
  32. 82
  33. 23
  34. 1521
  35. 9025
  36. 7
  37. 1764
  38. 16
  39. 100
  40. 34

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