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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 160 · 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 490 must be multiplied to get a perfect square?
  2. 2.A square garden has an area of 784 square m. How long is each side (in m)?
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √6400? =
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is 59²? =
  7. 7.How many whole numbers lie between 46² and 47²?
  8. 8.A square garden has an area of 1849 square m. How long is each side (in m)?
  9. 9.A square garden has an area of 1296 square m. How long is each side (in m)?
  10. 10.What is √9025? =
  11. 11.What is 49²? =
  12. 12.How many whole numbers lie between 13² and 14²?
  13. 13.A square garden has an area of 3025 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 12 must be divided to get a perfect square?
  15. 15.A square garden has an area of 1764 square m. How long is each side (in m)?
  16. 16.What is √7396? =
  17. 17.Which of these is a perfect square? (a) 523 (b) 484 (c) 509
  18. 18.What is √7569? =
  19. 19.Which of these is a perfect square? (a) 720 (b) 725 (c) 676
  20. 20.What is the smallest whole number by which 325 must be divided to get a perfect square?
  21. 21.What is √625? =
  22. 22.What is 75²? =
  23. 23.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.What is 68²? =
  26. 26.Which of these is a perfect square? (a) 324 (b) 347 (c) 340
  27. 27.How many whole numbers lie between 30² and 31²?
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  29. 29.Which of these is a perfect square? (a) 1604 (b) 1626 (c) 1600
  30. 30.A square garden has an area of 1024 square m. How long is each side (in m)?
  31. 31.What is 37²? =
  32. 32.What is 55²? =
  33. 33.Which of these is a perfect square? (a) 806 (b) 788 (c) 784
  34. 34.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 961 (b) 989 (c) 980
  36. 36.What is √1849? =
  37. 37.Which of these is a perfect square? (a) 400 (b) 434 (c) 402
  38. 38.How many whole numbers lie between 11² and 12²?
  39. 39.What is 23²? =
  40. 40.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 10
  2. 28
  3. 36
  4. 80
  5. 100
  6. 3481
  7. 92
  8. 43
  9. 36
  10. 95
  11. 2401
  12. 26
  13. 55
  14. 3
  15. 42
  16. 86
  17. 484
  18. 87
  19. 676
  20. 13
  21. 25
  22. 5625
  23. 144
  24. 64
  25. 4624
  26. 324
  27. 60
  28. 441
  29. 1600
  30. 32
  31. 1369
  32. 3025
  33. 784
  34. 11
  35. 961
  36. 43
  37. 400
  38. 22
  39. 529
  40. 361

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