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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 652 · 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) 1522 (b) 1521 (c) 1583
  2. 2.How many whole numbers lie between 44² and 45²?
  3. 3.What is √9604? =
  4. 4.What is the smallest whole number by which 44 must be divided to get a perfect square?
  5. 5.How many whole numbers lie between 35² and 36²?
  6. 6.Which of these is a perfect square? (a) 899 (b) 849 (c) 841
  7. 7.A square garden has an area of 3481 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 910 (b) 900 (c) 943
  10. 10.How many whole numbers lie between 9² and 10²?
  11. 11.A square garden has an area of 1369 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 196 square m. How long is each side (in m)?
  13. 13.What is √289? =
  14. 14.What is 39²? =
  15. 15.What is the smallest whole number by which 1134 must be divided to get a perfect square?
  16. 16.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
  17. 17.A square garden has an area of 121 square m. How long is each side (in m)?
  18. 18.What is √6084? =
  19. 19.Which of these is a perfect square? (a) 144 (b) 151 (c) 162
  20. 20.What is √676? =
  21. 21.What is √484? =
  22. 22.What is √784? =
  23. 23.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  24. 24.A square garden has an area of 484 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  27. 27.What is 79²? =
  28. 28.Which of these is a perfect square? (a) 1374 (b) 1421 (c) 1369
  29. 29.How many whole numbers lie between 48² and 49²?
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √8836? =
  32. 32.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 778 (b) 745 (c) 729
  34. 34.What is √256? =
  35. 35.A square garden has an area of 3600 square m. How long is each side (in m)?
  36. 36.Which of these is a perfect square? (a) 1296 (b) 1316 (c) 1298
  37. 37.What is 44²? =
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 820 (b) 835 (c) 784

Answer key

  1. 1521
  2. 88
  3. 98
  4. 11
  5. 70
  6. 841
  7. 59
  8. 144
  9. 900
  10. 18
  11. 37
  12. 14
  13. 17
  14. 1521
  15. 14
  16. 7
  17. 11
  18. 78
  19. 144
  20. 26
  21. 22
  22. 28
  23. 3
  24. 22
  25. 784
  26. 10
  27. 6241
  28. 1369
  29. 96
  30. 484
  31. 94
  32. 2
  33. 729
  34. 16
  35. 60
  36. 1296
  37. 1936
  38. 289
  39. 5
  40. 784

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