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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 448 · 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 √1444? =
  2. 2.What is 60²? =
  3. 3.A square garden has an area of 1521 square m. How long is each side (in m)?
  4. 4.What is 55²? =
  5. 5.What is √400? =
  6. 6.Which of these is a perfect square? (a) 1570 (b) 1521 (c) 1535
  7. 7.How many whole numbers lie between 19² and 20²?
  8. 8.How many whole numbers lie between 44² and 45²?
  9. 9.What is 59²? =
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is √3969? =
  12. 12.What is √576? =
  13. 13.What is √729? =
  14. 14.How many whole numbers lie between 45² and 46²?
  15. 15.Which of these is a perfect square? (a) 210 (b) 196 (c) 218
  16. 16.What is 78²? =
  17. 17.How many whole numbers lie between 12² and 13²?
  18. 18.What is √3721? =
  19. 19.What is √3364? =
  20. 20.What is √9025? =
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 27²? =
  23. 23.What is 97²? =
  24. 24.What is √169? =
  25. 25.What is 81²? =
  26. 26.Which of these is a perfect square? (a) 1089 (b) 1148 (c) 1147
  27. 27.Which of these is a perfect square? (a) 256 (b) 281 (c) 263
  28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  29. 29.Which of these is a perfect square? (a) 441 (b) 442 (c) 459
  30. 30.What is the smallest whole number by which 162 must be divided to get a perfect square?
  31. 31.A square garden has an area of 2704 square m. How long is each side (in m)?
  32. 32.A square garden has an area of 2304 square m. How long is each side (in m)?
  33. 33.What is the smallest whole number by which 375 must be divided to get a perfect square?
  34. 34.What is 44²? =
  35. 35.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 22² and 23²?
  39. 39.What is the smallest whole number by which 20 must be divided to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 324 (b) 325 (c) 350

Answer key

  1. 38
  2. 3600
  3. 39
  4. 3025
  5. 20
  6. 1521
  7. 38
  8. 88
  9. 3481
  10. 400
  11. 63
  12. 24
  13. 27
  14. 90
  15. 196
  16. 6084
  17. 24
  18. 61
  19. 58
  20. 95
  21. 361
  22. 729
  23. 9409
  24. 13
  25. 6561
  26. 1089
  27. 256
  28. 484
  29. 441
  30. 2
  31. 52
  32. 48
  33. 15
  34. 1936
  35. 2
  36. 6
  37. 81
  38. 44
  39. 5
  40. 324

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