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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 228 · 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 √441? =
  2. 2.Which of these is a perfect square? (a) 900 (b) 912 (c) 935
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 900 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 693 (b) 714 (c) 676
  6. 6.How many whole numbers lie between 20² and 21²?
  7. 7.What is √9604? =
  8. 8.What is 60²? =
  9. 9.How many whole numbers lie between 13² and 14²?
  10. 10.What is √576? =
  11. 11.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  12. 12.What is 66²? =
  13. 13.Which of these is a perfect square? (a) 1206 (b) 1180 (c) 1156
  14. 14.A square garden has an area of 100 square m. How long is each side (in m)?
  15. 15.What is √3844? =
  16. 16.Which of these is a perfect square? (a) 346 (b) 324 (c) 327
  17. 17.What is √8281? =
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  20. 20.A square garden has an area of 1225 square m. How long is each side (in m)?
  21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 21²? =
  24. 24.What is √9025? =
  25. 25.Which of these is a perfect square? (a) 1024 (b) 1033 (c) 1035
  26. 26.How many whole numbers lie between 16² and 17²?
  27. 27.A square garden has an area of 3136 square m. How long is each side (in m)?
  28. 28.Which of these is a perfect square? (a) 484 (b) 504 (c) 485
  29. 29.How many whole numbers lie between 5² and 6²?
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  31. 31.A square garden has an area of 1936 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 75 must be divided to get a perfect square?
  33. 33.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 810 must be divided to get a perfect square?
  35. 35.What is √6400? =
  36. 36.How many whole numbers lie between 14² and 15²?
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 208 must be divided to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 150 (b) 164 (c) 144
  40. 40.Which of these is a perfect square? (a) 100 (b) 108 (c) 102

Answer key

  1. 21
  2. 900
  3. 841
  4. 30
  5. 676
  6. 40
  7. 98
  8. 3600
  9. 26
  10. 24
  11. 10
  12. 4356
  13. 1156
  14. 10
  15. 62
  16. 324
  17. 91
  18. 441
  19. 10
  20. 35
  21. 784
  22. 144
  23. 441
  24. 95
  25. 1024
  26. 32
  27. 56
  28. 484
  29. 10
  30. 36
  31. 44
  32. 3
  33. 289
  34. 10
  35. 80
  36. 28
  37. 121
  38. 13
  39. 144
  40. 100

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