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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 266 · 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 468 must be divided to get a perfect square?
  2. 2.What is √5329? =
  3. 3.A square garden has an area of 2704 square m. How long is each side (in m)?
  4. 4.What is 18²? =
  5. 5.What is √7225? =
  6. 6.What is √225? =
  7. 7.Which of these is a perfect square? (a) 1265 (b) 1225 (c) 1245
  8. 8.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
  9. 9.A square garden has an area of 81 square m. How long is each side (in m)?
  10. 10.What is 14²? =
  11. 11.A square garden has an area of 3025 square m. How long is each side (in m)?
  12. 12.How many whole numbers lie between 12² and 13²?
  13. 13.What is 33²? =
  14. 14.What is √1225? =
  15. 15.What is the smallest whole number by which 162 must be divided to get a perfect square?
  16. 16.How many whole numbers lie between 5² and 6²?
  17. 17.How many whole numbers lie between 36² and 37²?
  18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
  20. 20.What is the smallest whole number by which 384 must be divided to get a perfect square?
  21. 21.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  22. 22.A square garden has an area of 1600 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 23² and 24²?
  24. 24.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  25. 25.What is 86²? =
  26. 26.How many whole numbers lie between 43² and 44²?
  27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 576 square m. How long is each side (in m)?
  29. 29.What is 76²? =
  30. 30.Which of these is a perfect square? (a) 1428 (b) 1369 (c) 1410
  31. 31.What is √1156? =
  32. 32.What is the smallest whole number by which 12 must be divided to get a perfect square?
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  34. 34.How many whole numbers lie between 21² and 22²?
  35. 35.What is √196? =
  36. 36.What is √1849? =
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  38. 38.Which of these is a perfect square? (a) 441 (b) 445 (c) 471
  39. 39.What is the smallest whole number by which 63 must be divided to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 561 (b) 529 (c) 573

Answer key

  1. 13
  2. 73
  3. 52
  4. 324
  5. 85
  6. 15
  7. 1225
  8. 6
  9. 9
  10. 196
  11. 55
  12. 24
  13. 1089
  14. 35
  15. 2
  16. 10
  17. 72
  18. 729
  19. 15
  20. 6
  21. 7
  22. 40
  23. 46
  24. 2
  25. 7396
  26. 86
  27. 441
  28. 24
  29. 5776
  30. 1369
  31. 34
  32. 3
  33. 25
  34. 42
  35. 14
  36. 43
  37. 400
  38. 441
  39. 7
  40. 529

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