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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 95 · 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 √400? =
  2. 2.What is the smallest whole number by which 48 must be divided to get a perfect square?
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  5. 5.Which of these is a perfect square? (a) 948 (b) 947 (c) 900
  6. 6.Which of these is a perfect square? (a) 511 (b) 487 (c) 484
  7. 7.A square garden has an area of 1089 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the smallest whole number by which 735 must be divided to get a perfect square?
  10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  11. 11.How many whole numbers lie between 8² and 9²?
  12. 12.A square garden has an area of 3025 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 1024 square m. How long is each side (in m)?
  14. 14.What is 18²? =
  15. 15.How many whole numbers lie between 7² and 8²?
  16. 16.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  17. 17.A square garden has an area of 441 square m. How long is each side (in m)?
  18. 18.Which of these is a perfect square? (a) 324 (b) 329 (c) 357
  19. 19.A square garden has an area of 2704 square m. How long is each side (in m)?
  20. 20.A square garden has an area of 49 square m. How long is each side (in m)?
  21. 21.A square garden has an area of 1936 square m. How long is each side (in m)?
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 81 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 1156 square m. How long is each side (in m)?
  25. 25.What is 63²? =
  26. 26.What is the smallest whole number by which 343 must be divided to get a perfect square?
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 1369 square m. How long is each side (in m)?
  29. 29.What is √5625? =
  30. 30.What is √1849? =
  31. 31.Which of these is a perfect square? (a) 1206 (b) 1204 (c) 1156
  32. 32.What is √2025? =
  33. 33.What is 65²? =
  34. 34.How many whole numbers lie between 6² and 7²?
  35. 35.A square garden has an area of 256 square m. How long is each side (in m)?
  36. 36.What is √441? =
  37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 40² and 41²?
  39. 39.What is 89²? =
  40. 40.What is 12²? =

Answer key

  1. 20
  2. 3
  3. 225
  4. 64
  5. 900
  6. 484
  7. 33
  8. 169
  9. 15
  10. 144
  11. 16
  12. 55
  13. 32
  14. 324
  15. 14
  16. 13
  17. 21
  18. 324
  19. 52
  20. 7
  21. 44
  22. 900
  23. 9
  24. 34
  25. 3969
  26. 7
  27. 81
  28. 37
  29. 75
  30. 43
  31. 1156
  32. 45
  33. 4225
  34. 12
  35. 16
  36. 21
  37. 484
  38. 80
  39. 7921
  40. 144

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