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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 79 · 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 √1156? =
  2. 2.What is √2809? =
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  4. 4.Which of these is a perfect square? (a) 111 (b) 100 (c) 117
  5. 5.What is √1849? =
  6. 6.What is 35²? =
  7. 7.Which of these is a perfect square? (a) 1281 (b) 1225 (c) 1257
  8. 8.What is 29²? =
  9. 9.What is the smallest whole number by which 117 must be divided to get a perfect square?
  10. 10.What is √196? =
  11. 11.How many whole numbers lie between 46² and 47²?
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  14. 14.How many whole numbers lie between 20² and 21²?
  15. 15.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  17. 17.What is the smallest whole number by which 125 must be divided to get a perfect square?
  18. 18.A square garden has an area of 3600 square m. How long is each side (in m)?
  19. 19.A square garden has an area of 361 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 225 (b) 231 (c) 241
  21. 21.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  22. 22.What is 27²? =
  23. 23.A square garden has an area of 2209 square m. How long is each side (in m)?
  24. 24.What is 58²? =
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is 26²? =
  27. 27.How many whole numbers lie between 48² and 49²?
  28. 28.A square garden has an area of 2025 square m. How long is each side (in m)?
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the smallest whole number by which 50 must be divided to get a perfect square?
  31. 31.Which of these is a perfect square? (a) 169 (b) 176 (c) 186
  32. 32.What is the smallest whole number by which 175 must be divided to get a perfect square?
  33. 33.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  34. 34.Which of these is a perfect square? (a) 835 (b) 784 (c) 798
  35. 35.What is the smallest whole number by which 45 must be divided to get a perfect square?
  36. 36.What is 14²? =
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  38. 38.How many whole numbers lie between 25² and 26²?
  39. 39.What is 40²? =
  40. 40.What is the smallest whole number by which 490 must be multiplied to get a perfect square?

Answer key

  1. 34
  2. 53
  3. 841
  4. 100
  5. 43
  6. 1225
  7. 1225
  8. 841
  9. 13
  10. 14
  11. 92
  12. 196
  13. 49
  14. 40
  15. 625
  16. 7
  17. 5
  18. 60
  19. 19
  20. 225
  21. 7
  22. 729
  23. 47
  24. 3364
  25. 324
  26. 676
  27. 96
  28. 45
  29. 64
  30. 2
  31. 169
  32. 7
  33. 11
  34. 784
  35. 5
  36. 196
  37. 361
  38. 50
  39. 1600
  40. 10

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