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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 240 · 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 50²? =
  2. 2.How many whole numbers lie between 35² and 36²?
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 15²? =
  5. 5.A square garden has an area of 2025 square m. How long is each side (in m)?
  6. 6.What is 32²? =
  7. 7.Which of these is a perfect square? (a) 1600 (b) 1667 (c) 1664
  8. 8.Which of these is a perfect square? (a) 944 (b) 922 (c) 900
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 68²? =
  11. 11.What is 56²? =
  12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  13. 13.Which of these is a perfect square? (a) 169 (b) 194 (c) 176
  14. 14.How many whole numbers lie between 13² and 14²?
  15. 15.What is √1849? =
  16. 16.What is the smallest whole number by which 1215 must be divided to get a perfect square?
  17. 17.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  18. 18.What is the smallest whole number by which 135 must be divided to get a perfect square?
  19. 19.How many whole numbers lie between 50² and 51²?
  20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 961 square m. How long is each side (in m)?
  22. 22.Which of these is a perfect square? (a) 1138 (b) 1089 (c) 1139
  23. 23.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 3249 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 384 must be divided to get a perfect square?
  26. 26.What is 33²? =
  27. 27.What is 92²? =
  28. 28.Which of these is a perfect square? (a) 484 (b) 494 (c) 496
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 810 must be divided to get a perfect square?
  31. 31.How many whole numbers lie between 16² and 17²?
  32. 32.A square garden has an area of 2401 square m. How long is each side (in m)?
  33. 33.What is √8100? =
  34. 34.How many whole numbers lie between 6² and 7²?
  35. 35.A square garden has an area of 2500 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1024 (b) 1040 (c) 1083
  37. 37.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  38. 38.What is 37²? =
  39. 39.What is 87²? =
  40. 40.What is 99²? =

Answer key

  1. 2500
  2. 70
  3. 400
  4. 225
  5. 45
  6. 1024
  7. 1600
  8. 900
  9. 49
  10. 4624
  11. 3136
  12. 676
  13. 169
  14. 26
  15. 43
  16. 15
  17. 2
  18. 15
  19. 100
  20. 20
  21. 31
  22. 1089
  23. 6
  24. 57
  25. 6
  26. 1089
  27. 8464
  28. 484
  29. 196
  30. 10
  31. 32
  32. 49
  33. 90
  34. 12
  35. 50
  36. 1024
  37. 13
  38. 1369
  39. 7569
  40. 9801

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