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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 402 · 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 √3249? =
  2. 2.What is √1600? =
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 16² and 17²?
  5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is 76²? =
  7. 7.What is √1156? =
  8. 8.What is the smallest whole number by which 126 must be divided to get a perfect square?
  9. 9.Which of these is a perfect square? (a) 256 (b) 257 (c) 274
  10. 10.Which of these is a perfect square? (a) 1156 (b) 1200 (c) 1209
  11. 11.What is 22²? =
  12. 12.How many whole numbers lie between 21² and 22²?
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 31² and 32²?
  15. 15.How many whole numbers lie between 38² and 39²?
  16. 16.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  17. 17.What is √5041? =
  18. 18.What is 92²? =
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 625 square m. How long is each side (in m)?
  21. 21.What is √1849? =
  22. 22.What is the smallest whole number by which 135 must be divided to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 1635 (b) 1623 (c) 1600
  24. 24.What is √1936? =
  25. 25.What is 87²? =
  26. 26.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 72²? =
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is √289? =
  31. 31.What is √9801? =
  32. 32.What is 12²? =
  33. 33.Which of these is a perfect square? (a) 1401 (b) 1369 (c) 1377
  34. 34.What is √1225? =
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  37. 37.What is √2304? =
  38. 38.Which of these is a perfect square? (a) 463 (b) 441 (c) 473
  39. 39.How many whole numbers lie between 6² and 7²?
  40. 40.How many whole numbers lie between 46² and 47²?

Answer key

  1. 57
  2. 40
  3. 25
  4. 32
  5. 784
  6. 5776
  7. 34
  8. 14
  9. 256
  10. 1156
  11. 484
  12. 42
  13. 144
  14. 62
  15. 76
  16. 6
  17. 71
  18. 8464
  19. 841
  20. 25
  21. 43
  22. 15
  23. 1600
  24. 44
  25. 7569
  26. 3
  27. 36
  28. 5184
  29. 256
  30. 17
  31. 99
  32. 144
  33. 1369
  34. 35
  35. 625
  36. 6
  37. 48
  38. 441
  39. 12
  40. 92

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