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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 476 · 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 sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is √784? =
  4. 4.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  5. 5.What is 75²? =
  6. 6.Which of these is a perfect square? (a) 498 (b) 484 (c) 490
  7. 7.What is the smallest whole number by which 350 must be divided to get a perfect square?
  8. 8.A square garden has an area of 2500 square m. How long is each side (in m)?
  9. 9.What is √5184? =
  10. 10.What is the smallest whole number by which 45 must be divided to get a perfect square?
  11. 11.What is the smallest whole number by which 504 must be divided to get a perfect square?
  12. 12.A square garden has an area of 1369 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 2116 square m. How long is each side (in m)?
  14. 14.What is 89²? =
  15. 15.How many whole numbers lie between 8² and 9²?
  16. 16.What is the smallest whole number by which 396 must be divided to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 378 (b) 386 (c) 361
  18. 18.What is 48²? =
  19. 19.How many whole numbers lie between 39² and 40²?
  20. 20.What is 80²? =
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  22. 22.A square garden has an area of 1089 square m. How long is each side (in m)?
  23. 23.Which of these is a perfect square? (a) 558 (b) 529 (c) 538
  24. 24.What is the smallest whole number by which 117 must be divided to get a perfect square?
  25. 25.What is √9801? =
  26. 26.What is √8464? =
  27. 27.How many whole numbers lie between 47² and 48²?
  28. 28.What is 66²? =
  29. 29.What is √3025? =
  30. 30.A square garden has an area of 121 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 147 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 126 must be divided to get a perfect square?
  34. 34.How many whole numbers lie between 22² and 23²?
  35. 35.What is 13²? =
  36. 36.What is √9216? =
  37. 37.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 20 must be divided to get a perfect square?
  39. 39.What is the smallest whole number by which 162 must be divided to get a perfect square?
  40. 40.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?

Answer key

  1. 400
  2. 256
  3. 28
  4. 3
  5. 5625
  6. 484
  7. 14
  8. 50
  9. 72
  10. 5
  11. 14
  12. 37
  13. 46
  14. 7921
  15. 16
  16. 11
  17. 361
  18. 2304
  19. 78
  20. 6400
  21. 289
  22. 33
  23. 529
  24. 13
  25. 99
  26. 92
  27. 94
  28. 4356
  29. 55
  30. 11
  31. 64
  32. 3
  33. 14
  34. 44
  35. 169
  36. 96
  37. 196
  38. 5
  39. 2
  40. 15

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