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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 127 · 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 162 must be multiplied to get a perfect square?
  2. 2.What is √1024? =
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 729 square m. How long is each side (in m)?
  6. 6.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  7. 7.Which of these is a perfect square? (a) 784 (b) 806 (c) 839
  8. 8.What is √1600? =
  9. 9.What is 16²? =
  10. 10.What is the smallest whole number by which 45 must be divided to get a perfect square?
  11. 11.What is √484? =
  12. 12.A square garden has an area of 576 square m. How long is each side (in m)?
  13. 13.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 42²? =
  15. 15.A square garden has an area of 529 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  17. 17.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  18. 18.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  19. 19.How many whole numbers lie between 16² and 17²?
  20. 20.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  21. 21.How many whole numbers lie between 8² and 9²?
  22. 22.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  23. 23.Which of these is a perfect square? (a) 328 (b) 324 (c) 343
  24. 24.Which of these is a perfect square? (a) 1444 (b) 1445 (c) 1453
  25. 25.A square garden has an area of 2209 square m. How long is each side (in m)?
  26. 26.Which of these is a perfect square? (a) 455 (b) 445 (c) 441
  27. 27.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  28. 28.What is 46²? =
  29. 29.What is 76²? =
  30. 30.What is 59²? =
  31. 31.A square garden has an area of 1849 square m. How long is each side (in m)?
  32. 32.A square garden has an area of 484 square m. How long is each side (in m)?
  33. 33.How many whole numbers lie between 14² and 15²?
  34. 34.What is 89²? =
  35. 35.What is 53²? =
  36. 36.What is 17²? =
  37. 37.How many whole numbers lie between 23² and 24²?
  38. 38.What is 25²? =
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  40. 40.A square garden has an area of 1089 square m. How long is each side (in m)?

Answer key

  1. 2
  2. 32
  3. 225
  4. 400
  5. 27
  6. 5
  7. 784
  8. 40
  9. 256
  10. 5
  11. 22
  12. 24
  13. 289
  14. 1764
  15. 23
  16. 3
  17. 15
  18. 2
  19. 32
  20. 25
  21. 16
  22. 10
  23. 324
  24. 1444
  25. 47
  26. 441
  27. 6
  28. 2116
  29. 5776
  30. 3481
  31. 43
  32. 22
  33. 28
  34. 7921
  35. 2809
  36. 289
  37. 46
  38. 625
  39. 64
  40. 33

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