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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 67 · 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.A square garden has an area of 144 square m. How long is each side (in m)?
  2. 2.What is √2304? =
  3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  5. 5.What is 41²? =
  6. 6.Which of these is a perfect square? (a) 462 (b) 441 (c) 461
  7. 7.What is √2209? =
  8. 8.How many whole numbers lie between 24² and 25²?
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √1156? =
  11. 11.What is √3364? =
  12. 12.How many whole numbers lie between 14² and 15²?
  13. 13.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  14. 14.A square garden has an area of 2209 square m. How long is each side (in m)?
  15. 15.Which of these is a perfect square? (a) 148 (b) 164 (c) 144
  16. 16.What is the smallest whole number by which 192 must be divided to get a perfect square?
  17. 17.What is √324? =
  18. 18.How many whole numbers lie between 42² and 43²?
  19. 19.A square garden has an area of 2500 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 206 (b) 196 (c) 205
  21. 21.What is √784? =
  22. 22.What is √1936? =
  23. 23.What is √441? =
  24. 24.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  25. 25.What is 17²? =
  26. 26.Which of these is a perfect square? (a) 121 (b) 139 (c) 122
  27. 27.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
  28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √400? =
  30. 30.How many whole numbers lie between 22² and 23²?
  31. 31.Which of these is a perfect square? (a) 256 (b) 262 (c) 275
  32. 32.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
  33. 33.What is 20²? =
  34. 34.What is 61²? =
  35. 35.What is 18²? =
  36. 36.What is the smallest whole number by which 325 must be divided to get a perfect square?
  37. 37.What is 92²? =
  38. 38.What is √5476? =
  39. 39.Which of these is a perfect square? (a) 805 (b) 819 (c) 784
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 12
  2. 48
  3. 64
  4. 5
  5. 1681
  6. 441
  7. 47
  8. 48
  9. 121
  10. 34
  11. 58
  12. 28
  13. 11
  14. 47
  15. 144
  16. 3
  17. 18
  18. 84
  19. 50
  20. 196
  21. 28
  22. 44
  23. 21
  24. 6
  25. 289
  26. 121
  27. 6
  28. 289
  29. 20
  30. 44
  31. 256
  32. 2
  33. 400
  34. 3721
  35. 324
  36. 13
  37. 8464
  38. 74
  39. 784
  40. 100

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