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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 662 · 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 18 must be divided to get a perfect square?
  2. 2.What is √4761? =
  3. 3.What is √5476? =
  4. 4.How many whole numbers lie between 23² and 24²?
  5. 5.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  6. 6.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  7. 7.A square garden has an area of 1369 square m. How long is each side (in m)?
  8. 8.Which of these is a perfect square? (a) 475 (b) 465 (c) 441
  9. 9.What is 52²? =
  10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 640 (b) 649 (c) 625
  13. 13.What is 51²? =
  14. 14.What is √7921? =
  15. 15.What is 62²? =
  16. 16.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  17. 17.Which of these is a perfect square? (a) 1574 (b) 1521 (c) 1543
  18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is the smallest whole number by which 468 must be divided to get a perfect square?
  20. 20.How many whole numbers lie between 40² and 41²?
  21. 21.How many whole numbers lie between 31² and 32²?
  22. 22.What is the smallest whole number by which 108 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 41² and 42²?
  24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √961? =
  26. 26.A square garden has an area of 81 square m. How long is each side (in m)?
  27. 27.What is 67²? =
  28. 28.A square garden has an area of 1089 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 256 square m. How long is each side (in m)?
  30. 30.What is √256? =
  31. 31.How many whole numbers lie between 47² and 48²?
  32. 32.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  33. 33.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  35. 35.Which of these is a perfect square? (a) 1600 (b) 1662 (c) 1627
  36. 36.What is √7744? =
  37. 37.A square garden has an area of 361 square m. How long is each side (in m)?
  38. 38.What is 59²? =
  39. 39.A square garden has an area of 1296 square m. How long is each side (in m)?
  40. 40.A square garden has an area of 1225 square m. How long is each side (in m)?

Answer key

  1. 2
  2. 69
  3. 74
  4. 46
  5. 15
  6. 7
  7. 37
  8. 441
  9. 2704
  10. 841
  11. 484
  12. 625
  13. 2601
  14. 89
  15. 3844
  16. 11
  17. 1521
  18. 121
  19. 13
  20. 80
  21. 62
  22. 3
  23. 82
  24. 729
  25. 31
  26. 9
  27. 4489
  28. 33
  29. 16
  30. 16
  31. 94
  32. 13
  33. 14
  34. 13
  35. 1600
  36. 88
  37. 19
  38. 3481
  39. 36
  40. 35

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