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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 13 · 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 sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  3. 3.How many whole numbers lie between 43² and 44²?
  4. 4.A square garden has an area of 1521 square m. How long is each side (in m)?
  5. 5.A square garden has an area of 1225 square m. How long is each side (in m)?
  6. 6.What is 21²? =
  7. 7.A square garden has an area of 1764 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 27²? =
  10. 10.What is 48²? =
  11. 11.How many whole numbers lie between 24² and 25²?
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  13. 13.Which of these is a perfect square? (a) 961 (b) 967 (c) 991
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √256? =
  16. 16.What is 88²? =
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  18. 18.What is the smallest whole number by which 117 must be divided to get a perfect square?
  19. 19.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 196 square m. How long is each side (in m)?
  21. 21.What is 93²? =
  22. 22.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 1600 square m. How long is each side (in m)?
  24. 24.What is the smallest whole number by which 243 must be divided to get a perfect square?
  25. 25.What is √400? =
  26. 26.A square garden has an area of 2304 square m. How long is each side (in m)?
  27. 27.What is 11²? =
  28. 28.What is 32²? =
  29. 29.What is the smallest whole number by which 350 must be divided to get a perfect square?
  30. 30.A square garden has an area of 625 square m. How long is each side (in m)?
  31. 31.What is the smallest whole number by which 27 must be divided to get a perfect square?
  32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  33. 33.How many whole numbers lie between 9² and 10²?
  34. 34.Which of these is a perfect square? (a) 216 (b) 199 (c) 196
  35. 35.How many whole numbers lie between 46² and 47²?
  36. 36.What is the smallest whole number by which 160 must be divided to get a perfect square?
  37. 37.What is √4624? =
  38. 38.Which of these is a perfect square? (a) 269 (b) 256 (c) 274
  39. 39.What is √3136? =
  40. 40.What is 98²? =

Answer key

  1. 36
  2. 5
  3. 86
  4. 39
  5. 35
  6. 441
  7. 42
  8. 25
  9. 729
  10. 2304
  11. 48
  12. 729
  13. 961
  14. 576
  15. 16
  16. 7744
  17. 225
  18. 13
  19. 5
  20. 14
  21. 8649
  22. 15
  23. 40
  24. 3
  25. 20
  26. 48
  27. 121
  28. 1024
  29. 14
  30. 25
  31. 3
  32. 81
  33. 18
  34. 196
  35. 92
  36. 10
  37. 68
  38. 256
  39. 56
  40. 9604

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