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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 41 · 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 26²? =
  2. 2.What is √121? =
  3. 3.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  4. 4.What is √4900? =
  5. 5.What is the smallest whole number by which 18 must be divided to get a perfect square?
  6. 6.What is √1225? =
  7. 7.What is √4489? =
  8. 8.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  9. 9.What is 53²? =
  10. 10.Which of these is a perfect square? (a) 937 (b) 936 (c) 900
  11. 11.Which of these is a perfect square? (a) 1677 (b) 1624 (c) 1600
  12. 12.Which of these is a perfect square? (a) 1296 (b) 1301 (c) 1307
  13. 13.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
  14. 14.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 421 (b) 400 (c) 410
  17. 17.What is 58²? =
  18. 18.What is 90²? =
  19. 19.A square garden has an area of 36 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 18² and 19²?
  21. 21.A square garden has an area of 1024 square m. How long is each side (in m)?
  22. 22.What is 96²? =
  23. 23.What is 91²? =
  24. 24.How many whole numbers lie between 28² and 29²?
  25. 25.Which of these is a perfect square? (a) 121 (b) 136 (c) 132
  26. 26.A square garden has an area of 576 square m. How long is each side (in m)?
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  28. 28.How many whole numbers lie between 12² and 13²?
  29. 29.How many whole numbers lie between 6² and 7²?
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the smallest whole number by which 176 must be divided to get a perfect square?
  32. 32.A square garden has an area of 1089 square m. How long is each side (in m)?
  33. 33.What is √7921? =
  34. 34.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  35. 35.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
  36. 36.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 35² and 36²?
  39. 39.What is the smallest whole number by which 490 must be divided to get a perfect square?
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 676
  2. 11
  3. 6
  4. 70
  5. 2
  6. 35
  7. 67
  8. 5
  9. 2809
  10. 900
  11. 1600
  12. 1296
  13. 10
  14. 15
  15. 529
  16. 400
  17. 3364
  18. 8100
  19. 6
  20. 36
  21. 32
  22. 9216
  23. 8281
  24. 56
  25. 121
  26. 24
  27. 64
  28. 24
  29. 12
  30. 121
  31. 11
  32. 33
  33. 89
  34. 14
  35. 10
  36. 2
  37. 289
  38. 70
  39. 10
  40. 100

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