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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 698 · 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 32²? =
  2. 2.How many whole numbers lie between 48² and 49²?
  3. 3.What is the smallest whole number by which 490 must be divided to get a perfect square?
  4. 4.What is √3025? =
  5. 5.How many whole numbers lie between 17² and 18²?
  6. 6.What is √7056? =
  7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 43²? =
  9. 9.What is √576? =
  10. 10.What is the smallest whole number by which 63 must be divided to get a perfect square?
  11. 11.What is 96²? =
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  15. 15.What is √1156? =
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 88²? =
  18. 18.A square garden has an area of 1369 square m. How long is each side (in m)?
  19. 19.What is 89²? =
  20. 20.What is √7396? =
  21. 21.What is √324? =
  22. 22.A square garden has an area of 1600 square m. How long is each side (in m)?
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.What is √6241? =
  26. 26.A square garden has an area of 3364 square m. How long is each side (in m)?
  27. 27.What is √400? =
  28. 28.Which of these is a perfect square? (a) 900 (b) 914 (c) 957
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  30. 30.Which of these is a perfect square? (a) 1218 (b) 1156 (c) 1193
  31. 31.What is 35²? =
  32. 32.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 894 (b) 841 (c) 865
  34. 34.Which of these is a perfect square? (a) 1555 (b) 1521 (c) 1564
  35. 35.What is √3844? =
  36. 36.What is 94²? =
  37. 37.A square garden has an area of 484 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 6² and 7²?
  39. 39.What is √169? =
  40. 40.Which of these is a perfect square? (a) 200 (b) 199 (c) 196

Answer key

  1. 1024
  2. 96
  3. 10
  4. 55
  5. 34
  6. 84
  7. 676
  8. 1849
  9. 24
  10. 7
  11. 9216
  12. 576
  13. 841
  14. 6
  15. 34
  16. 121
  17. 7744
  18. 37
  19. 7921
  20. 86
  21. 18
  22. 40
  23. 100
  24. 64
  25. 79
  26. 58
  27. 20
  28. 900
  29. 625
  30. 1156
  31. 1225
  32. 5
  33. 841
  34. 1521
  35. 62
  36. 8836
  37. 22
  38. 12
  39. 13
  40. 196

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