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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 330 · 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.Which of these is a perfect square? (a) 1001 (b) 961 (c) 966
  2. 2.How many whole numbers lie between 24² and 25²?
  3. 3.Which of these is a perfect square? (a) 344 (b) 352 (c) 324
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
  6. 6.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  7. 7.What is 75²? =
  8. 8.A square garden has an area of 1369 square m. How long is each side (in m)?
  9. 9.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  10. 10.Which of these is a perfect square? (a) 1649 (b) 1641 (c) 1600
  11. 11.What is the smallest whole number by which 250 must be divided to get a perfect square?
  12. 12.What is 32²? =
  13. 13.How many whole numbers lie between 44² and 45²?
  14. 14.How many whole numbers lie between 20² and 21²?
  15. 15.A square garden has an area of 1681 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 625 square m. How long is each side (in m)?
  17. 17.Which of these is a perfect square? (a) 103 (b) 100 (c) 108
  18. 18.What is the smallest whole number by which 704 must be divided to get a perfect square?
  19. 19.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  20. 20.What is 98²? =
  21. 21.A square garden has an area of 1156 square m. How long is each side (in m)?
  22. 22.What is √9216? =
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is 83²? =
  25. 25.What is 89²? =
  26. 26.What is √961? =
  27. 27.A square garden has an area of 400 square m. How long is each side (in m)?
  28. 28.What is √8649? =
  29. 29.What is √484? =
  30. 30.A square garden has an area of 2500 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  33. 33.What is 99²? =
  34. 34.A square garden has an area of 36 square m. How long is each side (in m)?
  35. 35.A square garden has an area of 2401 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 441 (b) 476 (c) 451
  37. 37.What is √1156? =
  38. 38.How many whole numbers lie between 37² and 38²?
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is √2209? =

Answer key

  1. 961
  2. 48
  3. 324
  4. 196
  5. 14
  6. 14
  7. 5625
  8. 37
  9. 7
  10. 1600
  11. 10
  12. 1024
  13. 88
  14. 40
  15. 41
  16. 25
  17. 100
  18. 11
  19. 13
  20. 9604
  21. 34
  22. 96
  23. 64
  24. 6889
  25. 7921
  26. 31
  27. 20
  28. 93
  29. 22
  30. 50
  31. 841
  32. 15
  33. 9801
  34. 6
  35. 49
  36. 441
  37. 34
  38. 74
  39. 441
  40. 47

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