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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 219 · 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.Which of these is a perfect square? (a) 1659 (b) 1638 (c) 1600
  2. 2.What is 41²? =
  3. 3.What is 56²? =
  4. 4.What is √2304? =
  5. 5.A square garden has an area of 2209 square m. How long is each side (in m)?
  6. 6.What is 35²? =
  7. 7.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 664 (b) 629 (c) 625
  9. 9.Which of these is a perfect square? (a) 566 (b) 570 (c) 529
  10. 10.A square garden has an area of 2116 square m. How long is each side (in m)?
  11. 11.How many whole numbers lie between 13² and 14²?
  12. 12.What is 68²? =
  13. 13.Which of these is a perfect square? (a) 129 (b) 121 (c) 143
  14. 14.What is the smallest whole number by which 490 must be divided to get a perfect square?
  15. 15.What is √7569? =
  16. 16.How many whole numbers lie between 16² and 17²?
  17. 17.A square garden has an area of 3600 square m. How long is each side (in m)?
  18. 18.What is √2209? =
  19. 19.A square garden has an area of 900 square m. How long is each side (in m)?
  20. 20.What is 99²? =
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  23. 23.A square garden has an area of 1024 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 1331 (b) 1327 (c) 1296
  25. 25.A square garden has an area of 2500 square m. How long is each side (in m)?
  26. 26.How many whole numbers lie between 8² and 9²?
  27. 27.What is 39²? =
  28. 28.A square garden has an area of 441 square m. How long is each side (in m)?
  29. 29.A square garden has an area of 49 square m. How long is each side (in m)?
  30. 30.A square garden has an area of 289 square m. How long is each side (in m)?
  31. 31.A square garden has an area of 729 square m. How long is each side (in m)?
  32. 32.What is the smallest whole number by which 448 must be divided to get a perfect square?
  33. 33.How many whole numbers lie between 18² and 19²?
  34. 34.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
  35. 35.What is √4900? =
  36. 36.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is 72²? =
  40. 40.What is 61²? =

Answer key

  1. 1600
  2. 1681
  3. 3136
  4. 48
  5. 47
  6. 1225
  7. 576
  8. 625
  9. 529
  10. 46
  11. 26
  12. 4624
  13. 121
  14. 10
  15. 87
  16. 32
  17. 60
  18. 47
  19. 30
  20. 9801
  21. 289
  22. 5
  23. 32
  24. 1296
  25. 50
  26. 16
  27. 1521
  28. 21
  29. 7
  30. 17
  31. 27
  32. 7
  33. 36
  34. 14
  35. 70
  36. 3
  37. 400
  38. 256
  39. 5184
  40. 3721

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