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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 398 · 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 √2304? =
  2. 2.What is √6561? =
  3. 3.What is 91²? =
  4. 4.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  5. 5.How many whole numbers lie between 14² and 15²?
  6. 6.What is √484? =
  7. 7.What is √625? =
  8. 8.How many whole numbers lie between 18² and 19²?
  9. 9.What is √1600? =
  10. 10.What is 44²? =
  11. 11.How many whole numbers lie between 15² and 16²?
  12. 12.A square garden has an area of 3136 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 2304 square m. How long is each side (in m)?
  14. 14.A square garden has an area of 1849 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 44² and 45²?
  16. 16.What is √6400? =
  17. 17.Which of these is a perfect square? (a) 1371 (b) 1387 (c) 1369
  18. 18.Which of these is a perfect square? (a) 133 (b) 121 (c) 129
  19. 19.What is the smallest whole number by which 686 must be divided to get a perfect square?
  20. 20.What is 80²? =
  21. 21.Which of these is a perfect square? (a) 324 (b) 358 (c) 328
  22. 22.What is √5776? =
  23. 23.How many whole numbers lie between 13² and 14²?
  24. 24.What is √2500? =
  25. 25.Which of these is a perfect square? (a) 169 (b) 183 (c) 172
  26. 26.Which of these is a perfect square? (a) 115 (b) 109 (c) 100
  27. 27.What is 62²? =
  28. 28.How many whole numbers lie between 46² and 47²?
  29. 29.What is 84²? =
  30. 30.What is the smallest whole number by which 117 must be divided to get a perfect square?
  31. 31.What is 56²? =
  32. 32.A square garden has an area of 1225 square m. How long is each side (in m)?
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  34. 34.A square garden has an area of 100 square m. How long is each side (in m)?
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is 40²? =
  37. 37.Which of these is a perfect square? (a) 1521 (b) 1538 (c) 1595
  38. 38.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 258 (b) 264 (c) 256
  40. 40.What is 88²? =

Answer key

  1. 48
  2. 81
  3. 8281
  4. 14
  5. 28
  6. 22
  7. 25
  8. 36
  9. 40
  10. 1936
  11. 30
  12. 56
  13. 48
  14. 43
  15. 88
  16. 80
  17. 1369
  18. 121
  19. 14
  20. 6400
  21. 324
  22. 76
  23. 26
  24. 50
  25. 169
  26. 100
  27. 3844
  28. 92
  29. 7056
  30. 13
  31. 3136
  32. 35
  33. 256
  34. 10
  35. 196
  36. 1600
  37. 1521
  38. 3
  39. 256
  40. 7744

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